A238625 Number of partitions p of n such that 1 + (1/2)*max(p) is a part of p.

0, 1, 1, 2, 2, 3, 4, 5, 6, 9, 11, 14, 19, 24, 31, 41, 51, 65, 84, 105, 132, 167, 207, 257, 321, 395, 486, 599, 731, 892, 1089, 1319, 1597, 1933, 2327, 2798, 3361, 4021, 4805, 5736, 6825, 8109, 9625, 11393, 13469, 15905, 18738, 22049, 25915, 30401, 35620

Offset: 1

Author

Clark Kimberling, Mar 02 2014

Keywords

• nonn
• easy

Examples

			a(6) counts these partitions:  222, 2211, 21111.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A238479, A238624.

Programs

Mathematica

Table[Count[IntegerPartitions[n], p_ /; MemberQ[p, 1 + Max[p]/2]], {n, 50}]
p[n_, m_] := If[m > n, 0, If[n == m, 1, p[n, m] = Sum[p[n - m, j], {j, m}]]]; a[1] = 0; a[n_] := 1 + Sum[p[n-k-1, 2*k], {k, n/2}]; Array[a,100] (* Giovanni Resta, Mar 07 2014 *)