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A288253 Number of heptagons that can be formed with perimeter n.

%I A288253 #33 Mar 10 2023 03:17:42
%S A288253 1,1,2,3,5,6,10,13,19,24,34,42,58,70,93,112,145,171,218,256,320,372,
%T A288253 458,528,643,735,884,1006,1198,1352,1597,1795,2102,2350,2732,3041,
%U A288253 3513,3892,4468,4934,5633,6194,7037,7715,8722,9531,10728,11690
%N A288253 Number of heptagons that can be formed with perimeter n.
%C A288253 Number of (a1, a2, ... , a7) where 1 <= a1 <= ... <= a7 and a1 + a2 + ... + a6 > a7.
%H A288253 Seiichi Manyama, <a href="/A288253/b288253.txt">Table of n, a(n) for n = 7..10000</a>
%H A288253 G. E. Andrews, P. Paule and A. Riese, <a href="http://www.risc.jku.at/publications/download/risc_163/PAIX.pdf">MacMahon's Partition Analysis IX: k-gon partitions</a>, Bull. Austral Math. Soc., 64 (2001), 321-329.
%H A288253 Geoffrey Critzer, <a href="https://esirc.emporia.edu/handle/123456789/3595">Combinatorics of Vector Spaces over Finite Fields</a>, Master's thesis, Emporia State University, 2018. [This thesis cites this sequence entry, but it's just a typo: the intended sequence entry is A288853.]
%H A288253 <a href="/index/Rec#order_49">Index entries for linear recurrences with constant coefficients</a>, 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).
%F A288253 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)).
%F A288253 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
%Y A288253 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).
%K A288253 nonn,easy
%O A288253 7,3
%A A288253 _Seiichi Manyama_, Jun 07 2017