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A068030 Number of subsets of {1,2,3,...,n} that sum to 0 mod 9. 2
1, 1, 1, 1, 2, 4, 8, 15, 30, 60, 116, 230, 458, 912, 1824, 3648, 7286, 14572, 29144, 58264, 116524, 233044, 466048, 932096, 1864192, 3728300, 7456600, 14913200, 29826224, 59652440, 119304872, 238609408, 477218816, 954437632, 1908874584 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Robert Israel, Table of n, a(n) for n = 0..3321

Mathematics StackExchange, Let S = 1,2,3,4,...,2070 find the number of subsets of S whose sum of elements in S is divisible by 9

Robert Israel, Proof of conjectured g.f.

FORMULA

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]

Empirical G.f. verified: see link. - Robert Israel, Apr 30 2019

MAPLE

G:= Array(0..100, 0..8):

G[0, 0]:= 1; for j from 1 to 8 do G[0, j]:= 0 od:

for n from 1 to 100 do

  for j from 0 to 8 do

     k:= j - n mod 9;

     G[n, j]:= G[n-1, j] + G[n-1, k];

od od:

seq(G[n, 0], n=0..100); # Robert Israel, Apr 30 2019

CROSSREFS

9th row of A068009.

Sequence in context: A189101 A018089 A124312 * A251707 A251712 A251742

Adjacent sequences:  A068027 A068028 A068029 * A068031 A068032 A068033

KEYWORD

nonn

AUTHOR

Antti Karttunen, Feb 11 2002

STATUS

approved

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Last modified October 23 04:06 EDT 2021. Contains 348211 sequences. (Running on oeis4.)