A245040 - OEIS

%I #7 May 01 2018 04:10:16

%S 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 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 28,34,40,42,41,52,46,55,59,64,58,81,70,82,85,92

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

%H Joerg Arndt and Alois P. Heinz, <a href="/A245040/b245040.txt">Table of n, a(n) for n = 9..1000</a>

%p b:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,

%p       b(n, i-1, k) +add(b(n-i*j, i-1, k), j=max(1, k)..n/i)))

%p     end:

%p a:= n-> b(n$2, 9) -b(n$2, 10):

%p seq(a(n), n=9..100);

%t 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 a[n_] := b[n, n, 9] - b[n, n, 10];

%t Table[a[n], {n, 9, 100}] (* _Jean-François Alcover_, May 01 2018, translated from Maple *)

%Y Column k=9 of A243978.

%K nonn

%O 9,19

%A _Joerg Arndt_ and _Alois P. Heinz_, Jul 10 2014