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