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A117298 Number of partitions of n with unique smallest part and unique largest part. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 25 23:17 EDT 2020. Contains 338026 sequences. (Running on oeis4.)