%I #4 Apr 14 2017 08:45:10
%S 0,1,2,7,17,47,121,320,835,2190,5730,15006,39282,102847,269252,704917,
%T 1845491,4831565,12649195,33116030,86698885,226980636,594243012,
%U 1555748412,4073002212,10663258237,27916772486,73087059235
%N Golden Triangle sums: a(n)=a(n-2)+A001654(n) with a(0)=0 and a(1)=1.
%C The a(n) are the Kn21, Kn22, Kn23, Fi2, and Ze2 sums of the Golden Triangle A180662. Furthermore the a(2*n) are the Kn3, Fi1 (terms doubled) and Ze3 (terms tripled) sums. See A180662 for information about these and other chess sums.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2, 3, -3, -2, 1).
%F a(n) = a(n-2)+A001654(n) with a(0)=0 and a(1)=1.
%F GF(x) = (-x)/((x-1)*(x+1)^2*(x^2-3*x+1)).
%F a(n) = ((-1)^(-n-1)*(15+10*n)-25+(16-4*A)*A^(-n-1)+(16-4*B)*B^(-n-1))/100 with A=(3+sqrt(5))/2 and B=(3-sqrt(5))/2.
%p nmax:=27: with(combinat): for n from 0 to nmax do A001654(n):=fibonacci(n)*fibonacci(n+1) od: a(0):=0: a(1):=1: for n from 2 to nmax do a(n) := a(n-2) + A001654(n) od: seq(a(n),n=0..nmax);
%Y Cf. A064831, A180664, A180665, A115730, A180666.
%K easy,nonn
%O 0,3
%A _Johannes W. Meijer_, Sep 21 2010