duplicates
N. J. A. Sloane
njas at research.att.com
Tue Jun 14 03:24:10 CEST 2005
Concerning Christian's message, I cannot resist mentioning
three sequences that I added to the OEIS yesterday - a strange
coincidence! Look:
%S A107755 2,8,12,26,30,36,38,80,84,90,92
%N A107755 Numbers n such that Sum_{k=1..n} Catalan(k) == 0 mod 3.
%D A107755 Y. More, Problem 11165, Amer. Math. Monthly, 112 (2002), 568.
%S A107756 1,4,5,6,7,10,13,14,15,16,17,18,19,20,21,22,23,24,25,28,31,32,33,34,37,
%T A107756 40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,
%U A107756 64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,82,85,86,87,88,91,94,95
%N A107756 Numbers n such that Sum_{k=1..n} Catalan(k) == 1 mod 3.
%D A107756 Y. More, Problem 11165, Amer. Math. Monthly, 112 (2002), 568.
%F A107756 Equivalently, numbers n such that base 3 expansion of n+1 contains a 2.
!!!!!!
%S A107757 3,9,11,27,29,35,39,81,83,89,93
%N A107757 Numbers n such that Sum_{k=1..n} Catalan(k) == 2 mod 3.
%D A107757 Y. More, Problem 11165, Amer. Math. Monthly, 112 (2002), 568.
I don't know if this is anything more than a coincidence. NJAS
>From seqfan-owner at ext.jussieu.fr Mon Jun 13 00:12:01 2005
>Date: Sun, 12 Jun 2005 21:09:41 -0700
>From: "Christian G.Bower" <bowerc at usa.net>
>To: seqfan <seqfan at ext.jussieu.fr>
>Subject: duplicates
>I'm looking at one that someone on the list might help with
>
>1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,1,1
>A039966 An example of a d-perfect sequence.
>A104405 Number of partitions of n into distinct powers of 3.
>??
>
>ID Number: A104405
>URL: http://www.research.att.com/projects/OEIS?Anum=A104405
>Sequence: 1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,1,
> 1,0,0,0,0,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
> 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,1,1,0,0,0,0,1,
> 1,0,1,1,0,0,0,0,0,0,0,0,0,0,0
>Name: Number of partitions of n into distinct powers of 3.
>
>can be described as characteristic function of numbers with no "2" !!!!!
>in their ternary representation
>
>ID Number: A039966
>URL: http://www.research.att.com/projects/OEIS?Anum=A039966
>Sequence: 1,0,1,1,0,0,0,0,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,1,
> 1
>Name: An example of a d-perfect sequence.
>
>can be described as A005043(n-1) mod 3
>
>ID Number: A005043 (Formerly M2587)
>URL: http://www.research.att.com/projects/OEIS?Anum=A005043
>Sequence: 1,0,1,1,3,6,15,36,91,232,603,1585,4213,11298,30537,83097,
> 227475,625992,1730787,4805595,13393689,37458330,105089229,
> 295673994,834086421,2358641376,6684761125,18985057351,
> 54022715451,154000562758
>Name: Motzkin sums: a(n) = (n-1)*(2*a(n-1)+3*a(n-2))/(n+1). Also called
> Riordan numbers or ring numbers.
>
>I've verified the 2 sequences match for the first 512 terms.
>
>Christian
>
>
>
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