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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. 10
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 (list; graph; refs; listen; history; text; internal format)
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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, May 05 2002
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)