|
%I #8 Aug 02 2022 22:03:10
%S 1,0,2,3,0,6,4,0,8,11,0,22,16,0,32,42,0,84,64,0,128,165,0,330,256,0,
%T 512,654,0,1308,1024,0,2048,2605,0,5210,4096,0,8192,10398,0,20796,
%U 16384,0,32768,41550,0,83100,65536,0,131072,166116,0,332232,262144,0
%N Number of solutions to c(0)F(0) + ... + c(n)F(n) = 0, where c(i) = +-1 for i >= 0, number of (+1)'s >= number of (-1)'s, F(i) = A000045(i) = Fibonacci numbers.
%F a(3n+1) = 0, a(A047270(n)) = A002083(n+5), a(A047238(n)) = 2^n.
%e a(3) = 3 because +0+1+1-2 = -0+1+1-2 = +0-1-1+2 = 0;
%e a(5) = 6 because +0+1-1-2-3+5 = +0-1+1-2-3+5 = +0+1-1+2+3-5 = -0+1-1+2+3-5 = +0-1+1+2+3-5 = -0-1+1+2+3-5 = 0.
%Y Cf. A000045, A002083, A047270, A047238.
%K nonn
%O 0,3
%A _Naohiro Nomoto_, Dec 08 2000
%E More terms from _Sean A. Irvine_, Aug 02 2022
|
