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A288254 Number of octagons that can be formed with perimeter n. 10
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
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
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Jun 07 2017
STATUS
approved

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Last modified March 28 08:22 EDT 2024. Contains 371236 sequences. (Running on oeis4.)