A237871 - OEIS

A237871

Number of partitions of n such that (greatest part) + (least part) > number of parts.

1, 2, 2, 4, 5, 8, 10, 16, 20, 28, 37, 51, 65, 88, 112, 147, 187, 243, 305, 391, 488, 618, 769, 963, 1189, 1479, 1817, 2241, 2739, 3357, 4081, 4976, 6021, 7296, 8794, 10605, 12728, 15284, 18272, 21845, 26024, 30996, 36797, 43671, 51676, 61118, 72106, 85013

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..48.

EXAMPLE

a(6) = 8 counts these partitions: 6, 51, 42, 411, 33, 321, 222, 3111..

MATHEMATICA

z = 60; q[n_] := q[n] = IntegerPartitions[n]; t[p_] := t[p] = Length[p];

Table[Count[q[n], p_ /; Max[p] + Min[p] < t[p]], {n, z}] (* A237822 *)

Table[Count[q[n], p_ /; Max[p] + Min[p] <= t[p]], {n, z}] (* A237823 *)

Table[Count[q[n], p_ /; Max[p] + Min[p] == t[p]], {n, z}] (* A237869 *)