A058301 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.

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, 512, 654, 0, 1308, 1024, 0, 2048, 2605, 0, 5210, 4096, 0, 8192, 10398, 0, 20796, 16384, 0, 32768, 41550, 0, 83100, 65536, 0, 131072, 166116, 0, 332232, 262144, 0

Offset

0,3

Links

Table of n, a(n) for n=0..55.

Formula

a(3n+1) = 0, a(A047270(n)) = A002083(n+5), a(A047238(n)) = 2^n.

Example

a(3) = 3 because +0+1+1-2 = -0+1+1-2 = +0-1-1+2 = 0;
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.

Crossrefs

Cf. A000045, A002083, A047270, A047238.

Sequence in context: A127468 A173720 A173717 * A199601 A231602 A097287

Adjacent sequences: A058298 A058299 A058300 * A058302 A058303 A058304

Keyword

nonn

Author

Naohiro Nomoto, Dec 08 2000

Extensions

More terms from Sean A. Irvine, Aug 02 2022

Status

approved