cp's OEIS Frontend

A068030 Number of subsets of {1,2,3,...,n} that sum to 0 mod 9.

%I A068030 #11 May 01 2019 05:33:28
%S A068030 1,1,1,1,2,4,8,15,30,60,116,230,458,912,1824,3648,7286,14572,29144,
%T A068030 58264,116524,233044,466048,932096,1864192,3728300,7456600,14913200,
%U A068030 29826224,59652440,119304872,238609408,477218816,954437632,1908874584
%N A068030 Number of subsets of {1,2,3,...,n} that sum to 0 mod 9.
%H A068030 Robert Israel, <a href="/A068030/b068030.txt">Table of n, a(n) for n = 0..3321</a>
%H A068030 Mathematics StackExchange, <a href="https://math.stackexchange.com/questions/3208526">Let S = 1,2,3,4,...,2070 find the number of subsets of S whose sum of elements in S is divisible by 9</a>
%H A068030 Robert Israel, <a href="/A068030/a068030.pdf">Proof of conjectured g.f.</a>
%F A068030 Empirical G.f.: -(4*x^12-2*x^9-x^7+2*x^6+2*x^5+2*x^4-3*x^3-x^2-x+1) / ((2*x-1)*(2*x^3-1)*(2*x^9-1)). [_Colin Barker_, Dec 22 2012]
%F A068030 Empirical G.f. verified: see link. - _Robert Israel_, Apr 30 2019
%p A068030 G:= Array(0..100, 0..8):
%p A068030 G[0,0]:= 1; for j from 1 to 8 do G[0,j]:= 0 od:
%p A068030 for n from 1 to 100 do
%p A068030   for j from 0 to 8 do
%p A068030      k:= j - n mod 9;
%p A068030      G[n,j]:= G[n-1,j] + G[n-1,k];
%p A068030 od od:
%p A068030 seq(G[n,0],n=0..100); # _Robert Israel_, Apr 30 2019
%Y A068030 9th row of A068009.
%K A068030 nonn
%O A068030 0,5
%A A068030 _Antti Karttunen_, Feb 11 2002