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A288253 revision #25

A288253

Number of heptagons that can be formed with perimeter n.

1, 1, 2, 3, 5, 6, 10, 13, 19, 24, 34, 42, 58, 70, 93, 112, 145, 171, 218, 256, 320, 372, 458, 528, 643, 735, 884, 1006, 1198, 1352, 1597, 1795, 2102, 2350, 2732, 3041, 3513, 3892, 4468, 4934, 5633, 6194, 7037, 7715, 8722, 9531, 10728, 11690

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OFFSET

7,3

COMMENTS

Number of (a1, a2, ... , a7) where 1 <= a1 <= ... <= a7 and a1 + a2 + ... + a6 > a7.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 7..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.

Geoffrey Critzer, Combinatorics of Vector Spaces over Finite Fields, master's thesis, 2018.

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

FORMULA

G.f.: x^7/((1-x)*(1-x^2)* ... *(1-x^7)) - x^12/(1-x) * 1/((1-x^2)*(1-x^4)* ... *(1-x^12)).

a(2*n+12) = A026813(2*n+12) - A288341(n), a(2*n+13) = A026813(2*n+13) - A288341(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), this sequence (k=7), A288254 (k=8), A288255 (k=9), A288256 (k=10).

Sequence in context: A341127 A087750 A341131 * A341154 A035959 A036801

Adjacent sequences: A288250 A288251 A288252 * A288254 A288255 A288256

KEYWORD

nonn,easy

AUTHOR

Seiichi Manyama, Jun 07 2017

STATUS

editing