|
%I #20 Jun 08 2017 10:42:23
%S 1,1,2,3,5,7,10,14,20,27,36,48,63,82,104,134,167,211,258,322,389,480,
%T 572,698,825,996,1165,1395,1620,1923,2216,2611,2991,3500,3984,4633,
%U 5248,6066,6836,7860,8820,10089,11273,12835,14288,16197
%N Number of octagons that can be formed with perimeter n.
%C Number of (a1, a2, ... , a8) where 1 <= a1 <= ... <= a8 and a1 + a2 + ... + a7 > a8.
%H Seiichi Manyama, <a href="/A288254/b288254.txt">Table of n, a(n) for n = 8..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_57">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, -1, 1, -1, 0, 0, 0, 0, -1, 1, 0, 0, -1, 1, -1, 1, 0, 0, 1, -1, 1, -1, 2, -2, 0, 0, 0, 0, 0, 0, -2, 2, -1, 1, -1, 1, 0, 0, 1, -1, 1, -1, 0, 0, 1, -1, 0, 0, 0, 0, -1, 1, -1, 1, 1, -1).
%F G.f.: x^8/((1-x)*(1-x^2)* ... *(1-x^8)) - x^14/(1-x) * 1/((1-x^2)*(1-x^4)* ... *(1-x^14)).
%F a(2*n+14) = A026814(2*n+14) - A288342(n), a(2*n+15) = A026814(2*n+15) - A288342(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), this sequence (k=8), A288255 (k=9), A288256 (k=10).
%K nonn,easy
%O 8,3
%A _Seiichi Manyama_, Jun 07 2017
|
