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A218511 Number of partitions of n in which any two parts differ by at most 9. 4

%I

%S 1,1,2,3,5,7,11,15,22,30,42,56,76,99,130,168,216,274,348,435,544,674,

%T 831,1017,1244,1507,1823,2193,2629,3136,3734,4420,5223,6148,7215,8438,

%U 9850,11453,13292,15382,17758,20447,23502,26935,30818,35181,40082,45570

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

%H Alois P. Heinz, <a href="/A218511/b218511.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: 1 + Sum_{j>0} x^j / Product_{i=0..9} (1-x^(i+j)).

%p b:= proc(n, i, k) option remember; `if`(n<0 or k<0, 0,

%p `if`(n=0, 1, `if`(i<1, 0, b(n, i-1, k-1) +b(n-i, i, k))))

%p end:

%p a:= n-> `if`(n=0, 1, 0) +add(b(n-i, i, 9), i=1..n):

%p seq(a(n), n=0..80);

%t 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 a[n_] := If[n == 0, 1, 0] + Sum[b[n - i, i, 9], {i, 1, n}];

%t Table[a[n], {n, 0, 80}] (* _Jean-Fran├žois Alcover_, May 20 2018, after _Alois P. Heinz_ *)

%Y Column k=9 of A194621.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Oct 31 2012

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Last modified June 18 06:02 EDT 2021. Contains 345098 sequences. (Running on oeis4.)