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

Author

Seiichi Manyama, Jun 07 2017

Keywords

• nonn
• easy

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).

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).

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.