# [seqfan] Re: A161984: obscure definition

Richard Mathar mathar at strw.leidenuniv.nl
Sun Jun 28 14:12:18 CEST 2009

```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

```