A069907 Number of hexagons that can be formed with perimeter n. In other words, partitions of n into six parts such that the sum of any 5 is more than the sixth.

0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 4, 6, 9, 12, 16, 22, 28, 37, 46, 59, 71, 91, 107, 134, 157, 193, 222, 271, 308, 371, 419, 499, 559, 661, 734, 860, 952, 1106, 1216, 1405, 1537, 1764, 1923, 2193, 2381, 2703, 2923, 3301, 3561, 4002, 4302, 4817, 5164

Offset

0,9

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from T. D. Noe)

G. E. Andrews, P. Paule and A. Riese, MacMahon's partition analysis III: The Omega package, European Journal of Combinatorics, Volume 22, Issue 7, October 2001, Pages 887-904.

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, 1, 1, -1, 0, -1, 0, 0, -1, 0, -1, 1, -1, 1, 1, 1, 1, -1, 1, -1, 0, -1, 0, 0, -1, 0, -1, 1, 1, 1, 0, -1).

Formula

G.f.: x^6*(1-x^4+x^5+x^7-x^8-x^13)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)*(1-x^6)*(1-x^8)*(1-x^10)).

a(2*n+10) = A026812(2*n+10) - A002622(n), a(2*n+11) = A026812(2*n+11) - A002622(n) for n >= 0. - Seiichi Manyama, Jun 08 2017

Prog

(PARI) concat(vector(6), Vec(x^6*(1-x^4+x^5+x^7-x^8-x^13)/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)*(1-x^6)*(1-x^8)*(1-x^10)) + O(x^80))) \\ Michel Marcus, Jun 24 2017

Crossrefs

Number of k-gons that can be formed with perimeter n: A005044 (k=3), A062890 (k=4), A069906 (k=5), this sequence (k=6), A288253 (k=7), A288254 (k=8), A288255 (k=9), A288256 (k=10).

Sequence in context: A305630 A371178 A271147 * A280424 A083365 A001935

Adjacent sequences: A069904 A069905 A069906 * A069908 A069909 A069910

Keyword

nonn,easy

Author

N. J. A. Sloane, May 05 2002

Status

approved