A288256 Number of decagons that can be formed with perimeter n.

1, 1, 2, 3, 5, 7, 11, 15, 21, 29, 40, 53, 71, 93, 121, 157, 200, 255, 321, 404, 500, 623, 762, 939, 1137, 1388, 1664, 2015, 2396, 2877, 3398, 4050, 4748, 5623, 6553, 7711, 8936, 10454, 12051, 14024, 16088, 18626, 21275, 24516, 27882, 31991, 36244, 41411, 46746

Offset

10,3

Comments

Number of (a1, a2, ... , a10) where 1 <= a1 <= ... <= a10 and a1 + a2 + ... + a9 > a10.

Links

Seiichi Manyama, Table of n, a(n) for n = 10..10000

G. E. Andrews, P. Paule and A. Riese, MacMahon's Partition Analysis IX: k-gon partitions, Bull. Austral Math. Soc., 64 (2001), 321-329.

Index entries for linear recurrences with constant coefficients, signature (0, 1, 0, 1, 1, 0, -1, 0, -1, -1, 0, 0, 0, -1, 1, 0, 0, 0, 1, -1, 0, 0, 0, 2, 1, 1, 0, 1, -2, 1, -1, 0, -1, -1, -1, -1, 0, -1, 1, -2, 1, -1, 1, -1, 2, 1, 1, 1, 1, 2, -1, 1, -1, 1, -2, 1, -1, 0, -1, -1, -1, -1, 0, -1, 1, -2, 1, 0, 1, 1, 2, 0, 0, 0, -1, 1, 0, 0, 0, 1, -1, 0, 0, 0, -1, -1, 0, -1, 0, 1, 1, 0, 1, 0, -1).

Formula

G.f.: x^10/((1-x)*(1-x^2)* ... *(1-x^10)) - x^18/(1-x) * 1/((1-x^2)*(1-x^4)* ... *(1-x^18)).

a(2*n+18) = A026816(2*n+18) - A288344(n), a(2*n+19) = A026816(2*n+19) - A288344(n) for n >= 0.

Crossrefs

Number of k-gons that can be formed with perimeter n: A005044 (k=3), A062890 (k=4), A069906 (k=5), A069907 (k=6), A288253 (k=7), A288254 (k=8), A288255 (k=9), this sequence (k=10).

Sequence in context: A232480 A332638 A035977 * A101049 A333193 A035986

Adjacent sequences: A288253 A288254 A288255 * A288257 A288258 A288259

Keyword

nonn,easy

Author

Seiichi Manyama, Jun 07 2017

Status

approved