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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.
0
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
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
KEYWORD
nonn
AUTHOR
Naohiro Nomoto, Dec 08 2000
EXTENSIONS
More terms from Sean A. Irvine, Aug 02 2022
STATUS
approved