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A245040 Number of partitions of n where the minimal multiplicity of any part is 9.

%I A245040 #7 May 01 2018 04:10:16
%S A245040 1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,2,1,2,1,2,1,2,1,2,3,3,2,4,2,3,3,
%T A245040 3,2,7,3,5,5,6,3,7,3,6,9,7,7,12,10,12,13,14,14,22,18,22,24,26,25,35,
%U A245040 28,34,40,42,41,52,46,55,59,64,58,81,70,82,85,92
%N A245040 Number of partitions of n where the minimal multiplicity of any part is 9.
%H A245040 Joerg Arndt and Alois P. Heinz, <a href="/A245040/b245040.txt">Table of n, a(n) for n = 9..1000</a>
%p A245040 b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A245040       b(n, i-1, k) +add(b(n-i*j, i-1, k), j=max(1, k)..n/i)))
%p A245040     end:
%p A245040 a:= n-> b(n$2, 9) -b(n$2, 10):
%p A245040 seq(a(n), n=9..100);
%t A245040 b[n_, i_, k_] := b[n, i, k] = If[n == 0, 1, If[i < 1, 0, b[n, i - 1, k] + Sum[b[n - i*j, i - 1, k], {j, Max[1, k], n/i}]]];
%t A245040 a[n_] := b[n, n, 9] - b[n, n, 10];
%t A245040 Table[a[n], {n, 9, 100}] (* _Jean-François Alcover_, May 01 2018, translated from Maple *)
%Y A245040 Column k=9 of A243978.
%K A245040 nonn
%O A245040 9,19
%A A245040 _Joerg Arndt_ and _Alois P. Heinz_, Jul 10 2014