[seqfan] Re: A161984: obscure definition
franktaw at netscape.net
franktaw at netscape.net
Sun Jun 28 21:34:47 CEST 2009
While we could do this, it seems to me to be a bit wrong-headed. I'm
not the author of these sequences, so I can't be sure, but it seems to
me that the intent is to associate a list of values with a key value
for each row. The standard way of doing this in the OEIS is to have a
tabl or tabf sequence, and let the row number make the association.
This suggests that A161985 "should" be:
%I A161985
%S A161985
1,2,3,4,3,4,5,6,7,4,5,6,7,8,9,10,5,6,7,8,9,10,11,12,13,6,7,8,9,10,11,12,
%T A161985
13,14,15,16,7,8,9,10,11,12,13,14,15,16,17,18,19,8,9,10,11,12,13,14,15,
%U A161985
16,17,18,19,20,21,22,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25
%N A161985 Table read by rows: the numbers from n+1 to 3n+1.
%C A161985 Row sums are (2n+1)^2.
%e A161985 The table starts:
%e A161985 1;
%e A161985 2,3,4;
%e A161985 3,4,5,6,7;
%e A161985 4,5,6,7,8,9,10;
%e A161985 5,6,7,8,9,10,11,12,13;
%Y A161985 Cf. A000027, A000290, A005408 (row lengths), A016754 (row
sums).
%K A161985 nonn,tabf,less,new
%O A161985 0,3
%A A161985 Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Jun 23 2009
%E A161985 Edited by R. J. Mathar (mathar(AT)strw.leidenuniv.nl) and
Franklin T.
Adams-Watters (FrankTAW(AT)Netscape.net) , Jun 28
2009
(Note, by the way, that the sequence in the database has an error in
the last row: 22,16,9 should be 22,17,9; this error is implicitly fixed
here.)
A similar transformation to A161984 produces just the odd numbers,
A005408. Perhaps a comment should be added to that sequence, something
like:
%C A005408 Regarded as a table, with n elements in row n, the row sum
for row n is n^3.
[Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Jun
23 2009]
and then A161984 can be deleted.
Franklin T. Adams-Watters
-----Original Message-----
From: Richard Mathar <mathar at strw.leidenuniv.nl>
As a followup to
http://list.seqfan.eu/pipermail/seqfan/2009-June/001792.html ,
we can make A161985 and A161984 a tabf and tabl to give it some
structure:
%I A161985
%S A161985
1,1,3,2,3,4,5,3,4,5,6,7,7,4,5,6,7,8,9,10,9,5,6,7,8,9,10,11,12,13,11,6,
%T A161985
7,8,9,10,11,12,13,14,15,16,13,7,8,9,10,11,12,13,14,15,16,17,18,19,15,8,
%U A161985
9,10,11,12,13,14,15,16,17,18,19,20,21,22,16,9,10,11,12,13,14,15,16,17
%N A161985 Table read by rows: the number 2n+1 followed by the numbers
n+1 to
3n+1.
%C A161985 Row sums are 2(n+1)(2n+1). Row sums discarding the first
column are
(2n+1)^2,
%C A161985 that is the square of the element in the first column.
%e A161985 The table with rows starting at n=0 is
%e A161985 1,1;
%e A161985 3,2,3,4;
%e A161985 5,3,4,5,6,7;
%e A161985 7,4,5,6,7,8,9,10;
%e A161985 9,5,6,7,8,9,10,11,12,13;
%Y A161985 Cf. A000027, A000290.
%K A161985 nonn,tabf,less,new
%O A161985 0,3
%A A161985 Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Jun 23 2009
%E A161985 Edited by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun
28 2009
%I A161984
%S A161984
0,1,1,2,3,5,3,7,9,11,4,13,15,17,19,5,21,23,25,27,29,6,31,33,35,37,39,
%T A161984
41,7,43,45,47,49,51,53,55,8,57,59,61,63,65,67,69,71,9,73,75,77,79,81,
%U A161984
83,85,87,89,10,91,93,95,97,99,101,103,105,107,109,11,111,113,115,117
%N A161984 Table read by rows: the number n followed by the odd numbers
from
n(n-1)+1 to (n-1)(n+2)+1.
%C A161984 The second column is A002061. The last element of row n is
A028387(n-1).
%C A161984 Row sums discarding the first column are n^3, that is the
cube of the
element in the first column.
%e A161984 The table with rows starting at n=0 is
%e A161984 0;
%e A161984 1,1;
%e A161984 2,3,5;
%e A161984 3,7,9,11;
%e A161984 4,13,15,17,19;
%e A161984 5,21,23,25,27,29;
%e A161984 6,31,33,35,37,39,41;
%e A161984 7,43,45,47,49,51,53,55;
%e A161984 8,57,59,61,63,65,67,69,71;
%e A161984 9,73,75,77,79,81,83,85,87,89;
%e A161984 10,91,93,95,,97,99,101,103,105,107,109;
%Y A161984 Cf. A000027, A000578.
%K A161984 nonn,tabl,less,new
%O A161984 0,4
%A A161984 Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Jun 23 2009
%A A161984 Edited by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun
28 2009
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