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A349451
Dirichlet inverse of Fibonacci numbers, when started from A000045(1): 1, 1, 2, 3, 5, 8, 13, 21, ...
5
1, -1, -2, -2, -5, -4, -13, -16, -30, -45, -89, -122, -233, -351, -590, -944, -1597, -2496, -4181, -6640, -10894, -17533, -28657, -46000, -75000, -120927, -196290, -317018, -514229, -830580, -1346269, -2176288, -3524222, -5699693, -9227335, -14924550, -24157817, -39079807, -63245054, -102320320, -165580141, -267890844
OFFSET
1,3
LINKS
FORMULA
a(1) = 1; a(n) = -Sum_{d|n, d < n} A000045(n/d) * a(d).
G.f. A(x) satisfies: A(x) = x - Sum_{k>=2} Fibonacci(k) * A(x^k). - Ilya Gutkovskiy, Feb 23 2022
MATHEMATICA
a[1] = 1; a[n_] := a[n] = -DivisorSum[n, a[#] * Fibonacci[n/#] &, # < n &]; Array[a, 42] (* Amiram Eldar, Nov 22 2021 *)
PROG
(PARI)
memoA349451 = Map();
A349451(n) = if(1==n, 1, my(v); if(mapisdefined(memoA349451, n, &v), v, v = -sumdiv(n, d, if(d<n, fibonacci(n/d)*A349451(d), 0)); mapput(memoA349451, n, v); (v)));
CROSSREFS
KEYWORD
sign
AUTHOR
Antti Karttunen, Nov 22 2021
STATUS
approved