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%I #29 Jun 24 2017 06:54:36
%S 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,
%T 222,271,308,371,419,499,559,661,734,860,952,1106,1216,1405,1537,1764,
%U 1923,2193,2381,2703,2923,3301,3561,4002,4302,4817,5164
%N 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.
%H Seiichi Manyama, <a href="/A069907/b069907.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..1000 from T. D. Noe)
%H G. E. Andrews, P. Paule and A. Riese, <a href="https://doi.org/10.1006/eujc.2001.0527">MacMahon's partition analysis III: The Omega package</a>, European Journal of Combinatorics, Volume 22, Issue 7, October 2001, Pages 887-904.
%H G. E. Andrews, P. Paule and A. Riese, <a href="https://doi.org/10.1017/S0004972700039988">MacMahon's Partition Analysis IX: k-gon partitions</a>, Bull. Austral Math. Soc., 64 (2001), 321-329.
%H <a href="/index/Rec#order_33">Index entries for linear recurrences with constant coefficients</a>, 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).
%F 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)).
%F 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
%o (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
%Y 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).
%K nonn,easy
%O 0,9
%A _N. J. A. Sloane_, May 05 2002
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