A288254 Number of octagons that can be formed with perimeter n.

1, 1, 2, 3, 5, 7, 10, 14, 20, 27, 36, 48, 63, 82, 104, 134, 167, 211, 258, 322, 389, 480, 572, 698, 825, 996, 1165, 1395, 1620, 1923, 2216, 2611, 2991, 3500, 3984, 4633, 5248, 6066, 6836, 7860, 8820, 10089, 11273, 12835, 14288, 16197

Offset: 8

Author

Seiichi Manyama, Jun 07 2017

Keywords

• nonn
• easy

Comments

Number of (a1, a2, ... , a8) where 1 <= a1 <= ... <= a8 and a1 + a2 + ... + a7 > a8.

Links

• Seiichi Manyama, Table of n, a(n) for n = 8..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 (1, 1, -1, 1, -1, 0, 0, 0, 0, -1, 1, 0, 0, -1, 1, -1, 1, 0, 0, 1, -1, 1, -1, 2, -2, 0, 0, 0, 0, 0, 0, -2, 2, -1, 1, -1, 1, 0, 0, 1, -1, 1, -1, 0, 0, 1, -1, 0, 0, 0, 0, -1, 1, -1, 1, 1, -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), this sequence (k=8), A288255 (k=9), A288256 (k=10).

Formula

G.f.: x^8/((1-x)*(1-x^2)* ... *(1-x^8)) - x^14/(1-x) * 1/((1-x^2)*(1-x^4)* ... *(1-x^14)).

a(2*n+14) = A026814(2*n+14) - A288342(n), a(2*n+15) = A026814(2*n+15) - A288342(n) for n >= 0. - Seiichi Manyama, Jun 08 2017