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A218511 Number of partitions of n in which any two parts differ by at most 9.

%I A218511 #13 May 20 2018 11:35:04
%S A218511 1,1,2,3,5,7,11,15,22,30,42,56,76,99,130,168,216,274,348,435,544,674,
%T A218511 831,1017,1244,1507,1823,2193,2629,3136,3734,4420,5223,6148,7215,8438,
%U A218511 9850,11453,13292,15382,17758,20447,23502,26935,30818,35181,40082,45570
%N A218511 Number of partitions of n in which any two parts differ by at most 9.
%H A218511 Alois P. Heinz, <a href="/A218511/b218511.txt">Table of n, a(n) for n = 0..1000</a>
%F A218511 G.f.: 1 + Sum_{j>0} x^j / Product_{i=0..9} (1-x^(i+j)).
%p A218511 b:= proc(n, i, k) option remember; `if`(n<0 or k<0, 0,
%p A218511       `if`(n=0, 1, `if`(i<1, 0, b(n, i-1, k-1) +b(n-i, i, k))))
%p A218511     end:
%p A218511 a:= n-> `if`(n=0, 1, 0) +add(b(n-i, i, 9), i=1..n):
%p A218511 seq(a(n), n=0..80);
%t A218511 b[n_, i_, k_] := b[n, i, k] = If[n < 0 || k < 0, 0, If[n == 0, 1, If[i < 1, 0, b[n, i - 1, k - 1] + b[n - i, i, k]]]];
%t A218511 a[n_] := If[n == 0, 1, 0] + Sum[b[n - i, i, 9], {i, 1, n}];
%t A218511 Table[a[n], {n, 0, 80}] (* _Jean-François Alcover_, May 20 2018, after _Alois P. Heinz_ *)
%Y A218511 Column k=9 of A194621.
%K A218511 nonn
%O A218511 0,3
%A A218511 _Alois P. Heinz_, Oct 31 2012