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A096740 Number of partitions of n into distinct parts >= 11.

%I A096740 #21 Nov 24 2020 16:40:02
%S A096740 1,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,2,2,3,3,4,4,5,5,6,6,7,
%T A096740 7,8,9,10,11,13,14,16,18,20,22,25,27,30,33,36,40,44,48,53,59,64,71,78,
%U A096740 86,94,104,113,125,136,149,163,179,194,213,232,254,276,302,328,359,390,425
%N A096740 Number of partitions of n into distinct parts >= 11.
%C A096740 The old entry with this sequence number was a duplicate of A071569.
%H A096740 Alois P. Heinz, <a href="/A096740/b096740.txt">Table of n, a(n) for n = 0..1000</a>
%F A096740 a(n) = A026831(n+10). - _R. J. Mathar_, Jul 31 2008
%F A096740 G.f.: Product_{j>=11} (1+x^j). - _R. J. Mathar_, Jul 31 2008
%F A096740 G.f.: Sum_{k>=0} x^(k*(k + 21)/2) / Product_{j=1..k} (1 - x^j). - _Ilya Gutkovskiy_, Nov 24 2020
%p A096740 b:= proc(n, i) option remember;
%p A096740       `if`(n=0, 1, `if`((i-10)*(i+11)/2<n, 0,
%p A096740        add(b(n-i*j, i-1), j=0..min(1, n/i))))
%p A096740     end:
%p A096740 a:= n-> b(n$2):
%p A096740 seq(a(n), n=0..100);  # _Alois P. Heinz_, Feb 07 2014
%t A096740 d[n_] := Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 && Min[#] >= 11 &]; Table[d[n], {n, 30}] (* str partitions, parts >= 11 *)
%t A096740 Table[Length[d[n]], {n, 40}] (* A096740 for n >= 1 *)
%t A096740 (* _Clark Kimberling_, Mar 07 2014 *)
%t A096740 b[n_, i_] := b[n, i] = If[n == 0, 1, If[(i-10)*(i+11)/2 < n, 0, Sum[b[n - i*j, i-1], {j, 0, Min[1, n/i]}]]]; a[n_] := b[n, n]; Table[a[n], {n, 0, 100}] (* _Jean-François Alcover_, Nov 11 2015, after _Alois P. Heinz_ *)
%Y A096740 Cf. A025147.
%K A096740 nonn
%O A096740 0,24
%A A096740 _N. J. A. Sloane_, Sep 28 2008