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A023655
Convolution of (F(2), F(3), F(4), ...) and A023533.
1
1, 2, 3, 6, 10, 16, 26, 42, 68, 111, 180, 291, 471, 762, 1233, 1995, 3228, 5223, 8451, 13675, 22127, 35802, 57929, 93731, 151660, 245391, 397051, 642442, 1039493, 1681935, 2721428, 4403363, 7124791
OFFSET
1,2
LINKS
FORMULA
a(n) = Sum_{k=0..n-1} Fibonacci(k+2) * A023533(n-k), n >= 1. - G. C. Greubel, Jul 16 2022
MATHEMATICA
Table[Sum[Fibonacci[m+1 -Binomial[j+3, 3]], {j, 0, n}], {n, 0, 5}, {m, Binomial[n+3, 3] +1, Binomial[n+4, 3]}]//Flatten (* G. C. Greubel, Jul 16 2022 *)
PROG
(Magma)
A023533:= func< n | Binomial(Floor((6*n-1)^(1/3)) +2, 3) ne n select 0 else 1 >;
[(&+[Fibonacci(k+2)*A023533(n-k): k in [0..n-1]]): n in [1..50]]; // G. C. Greubel, Jul 16 2022
(SageMath)
def A023655(n, k): return sum(fibonacci(k+1-binomial(j+3, 3)) for j in (0..n))
flatten([[A023655(n, k) for k in (binomial(n+3, 3)+1..binomial(n+4, 3))] for n in (0..5)]) # G. C. Greubel, Jul 16 2022
CROSSREFS
Essentially the same as A023613.
Sequence in context: A262984 A201077 A355383 * A354210 A023561 A243735
KEYWORD
nonn
STATUS
approved