A288254 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

8,3

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).

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

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).

Sequence in context: A237269 A116634 A035960 * A023893 A065094 A145728

Adjacent sequences: A288251 A288252 A288253 * A288255 A288256 A288257

KEYWORD

nonn,easy

AUTHOR

Seiichi Manyama, Jun 07 2017

STATUS

approved