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%I #18 Jun 08 2017 10:43:43
%S 1,1,2,3,5,7,11,14,21,28,39,50,69,87,116,145,189,233,299,363,458,553,
%T 687,820,1009,1195,1453,1709,2058,2404,2872,3331,3948,4557,5361,6152,
%U 7194,8215,9547,10853,12543,14199,16329,18407,21067,23666,26964,30179,34248,38207
%N Number of nonagons that can be formed with perimeter n.
%C Number of (a1, a2, ... , a9) where 1 <= a1 <= ... <= a9 and a1 + a2 + ... + a8 > a9.
%H Seiichi Manyama, <a href="/A288255/b288255.txt">Table of n, a(n) for n = 9..10000</a>
%H 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 <a href="/index/Rec#order_81">Index entries for linear recurrences with constant coefficients</a>, signature (0, 1, 0, 1, 0, 0, 0, 0, 1, -1, -1, 0, -1, -1, 0, 0, 0, -1, 1, 0, 0, 1, 1, 2, 0, 1, 1, 0, 0, 1, -1, -1, -2, -1, -1, -2, 0, -1, -1, -1, 1, 1, 1, 0, 2, 1, 1, 2, 1, 1, -1, 0, 0, -1, -1, 0, -2, -1, -1, 0, 0, -1, 1, 0, 0, 0, 1, 1, 0, 1, 1, -1, 0, 0, 0, 0, -1, 0, -1, 0, 1).
%F G.f.: x^9/((1-x)*(1-x^2)* ... *(1-x^9)) - x^16/(1-x) * 1/((1-x^2)*(1-x^4)* ... *(1-x^16)).
%F a(2*n+16) = A026815(2*n+16) - A288343(n), a(2*n+17) = A026815(2*n+17) - A288343(n) for n >= 0. - _Seiichi Manyama_, Jun 08 2017
%Y Number of k-gons that can be formed with perimeter n: A005044 (k=3), A062890 (k=4), A069906 (k=5), A069907 (k=6), A288253 (k=7), A288254 (k=8), this sequence (k=9), A288256 (k=10).
%K nonn,easy
%O 9,3
%A _Seiichi Manyama_, Jun 07 2017
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