%I #19 Jun 09 2017 03:27:20

%S 1,1,2,3,5,7,11,15,21,29,40,53,71,93,121,157,200,255,321,404,500,623,

%T 762,939,1137,1388,1664,2015,2396,2877,3398,4050,4748,5623,6553,7711,

%U 8936,10454,12051,14024,16088,18626,21275,24516,27882,31991,36244,41411,46746

%N Number of decagons that can be formed with perimeter n.

%C Number of (a1, a2, ... , a10) where 1 <= a1 <= ... <= a10 and a1 + a2 + ... + a9 > a10.

%H Seiichi Manyama, <a href="/A288256/b288256.txt">Table of n, a(n) for n = 10..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_95">Index entries for linear recurrences with constant coefficients</a>, signature (0, 1, 0, 1, 1, 0, -1, 0, -1, -1, 0, 0, 0, -1, 1, 0, 0, 0, 1, -1, 0, 0, 0, 2, 1, 1, 0, 1, -2, 1, -1, 0, -1, -1, -1, -1, 0, -1, 1, -2, 1, -1, 1, -1, 2, 1, 1, 1, 1, 2, -1, 1, -1, 1, -2, 1, -1, 0, -1, -1, -1, -1, 0, -1, 1, -2, 1, 0, 1, 1, 2, 0, 0, 0, -1, 1, 0, 0, 0, 1, -1, 0, 0, 0, -1, -1, 0, -1, 0, 1, 1, 0, 1, 0, -1).

%F G.f.: x^10/((1-x)*(1-x^2)* ... *(1-x^10)) - x^18/(1-x) * 1/((1-x^2)*(1-x^4)* ... *(1-x^18)).

%F a(2*n+18) = A026816(2*n+18) - A288344(n), a(2*n+19) = A026816(2*n+19) - A288344(n) for n >= 0.

%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), A288255 (k=9), this sequence (k=10).

%K nonn,easy

%O 10,3

%A _Seiichi Manyama_, Jun 07 2017