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

1,3

Links

Table of n, a(n) for n=1..51.

Formula

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

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

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 *)

Crossrefs

Sequence in context: A094991 A255575 A225501 * A274200 A018052 A018124

Adjacent sequences: A117295 A117296 A117297 * A117299 A117300 A117301

Keyword

easy,nonn

Author

Emeric Deutsch and Vladeta Jovovic, Apr 23 2006

Extensions

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

Status

approved