A117298 Number of partitions of n with unique smallest part and unique largest part.

1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 15, 21, 25, 34, 42, 55, 67, 88, 106, 137, 166, 210, 254, 320, 384, 478, 575, 708, 848, 1039, 1239, 1507, 1795, 2167, 2574, 3094, 3661, 4378, 5171, 6153, 7246, 8591, 10088, 11914, 13960, 16424, 19197, 22519, 26253, 30701, 35718

Offset: 1

Author

Emeric Deutsch and Vladeta Jovovic, Apr 23 2006

Keywords

• easy
• nonn

Programs

Mathematica

(* first do *) Needs["DiscreteMath`Combinatorica`"] (* then *) f[n_] := Block[{p = Partitions@n, q = PartitionsP@n, c = 0, k = 1}, While[k < q, s = Split@ p[[k]]; If[Length@First@s == 1 && Length@Last@s == 1, c++ ]; k++ ]; c]; Array[f, 51] (* Robert G. Wilson v *)

Formula

a(2*n+1)= A002865(2*n+1)+1, a(2*n)= A002865(2*n).

a(n) = A117995(n)+1.

Extensions

More terms from Robert G. Wilson v, Apr 25 2006