cp's OEIS Frontend

A238607 Number of partitions p of 2n such that n - (number of parts of p) is a part of p.

%I A238607 #14 Jul 20 2019 01:17:06
%S A238607 0,0,1,4,12,24,49,85,147,232,374,558,843,1223,1774,2493,3519,4835,
%T A238607 6659,8999,12144,16152,21479,28186,36945,47959,62126,79805,102352,
%U A238607 130286,165546,209070,263461,330266,413207,514486,639342,791261,977301,1202636,1477172
%N A238607 Number of partitions p of 2n such that n - (number of parts of p) is a part of p.
%H A238607 Giovanni Resta, <a href="/A238607/b238607.txt">Table of n, a(n) for n = 1..1000</a>
%e A238607 a(4) counts these partitions of 8:  62, 611, 521, 431.
%t A238607 z = 30; g[n_] := IntegerPartitions[n]; m[p_, t_] := MemberQ[p, t];
%t A238607 Table[Count[g[2 n], p_ /; m[p, n - Length[p]]], {n, z}] (*A238607*)
%t A238607 Table[Count[g[2 n - 1], p_ /; m[p, n - Length[p]]], {n, z}] (*A238641*)
%t A238607 Table[Count[g[2 n + 1], p_ /; m[p, n - Length[p]]], {n, z}] (*A238742*)
%t A238607 p[n_, k_] := p[n, k] = If[k == 1 || n == k, 1, If[k > n, 0, p[n-1, k-1] + p[n-k, k]]]; q[n_, k_, e_] := If[n-e < k-1, 0, If[k == 1, If[n == e, 1, 0], p[n-e, k-1]]]; a[n_] := Sum[q[2*n, u, n-u], {u, n-1}]; Array[a, 100] (* _Giovanni Resta_, Mar 07 2014 *)
%Y A238607 Cf. A238641, A238742.
%K A238607 nonn,easy
%O A238607 1,4
%A A238607 _Clark Kimberling_, Mar 04 2014
%E A238607 More terms from _Alois P. Heinz_, Mar 04 2014