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A023623
Convolution of Lucas numbers and A023533.
1
1, 3, 4, 8, 14, 22, 36, 58, 94, 153, 249, 402, 651, 1053, 1704, 2757, 4461, 7218, 11679, 18898, 30579, 49477, 80056, 129533, 209589, 339122, 548711, 887833, 1436544, 2324377, 3760921, 6085298, 9846219
OFFSET
1,2
LINKS
FORMULA
a(n) = Sum_{j=1..n+1} LucasL(j) * A023533(n-j+1). - G. C. Greubel, Jul 16 2022
MATHEMATICA
Table[Sum[LucasL[m+2-Binomial[j+3, 3]], {j, 0, n}], {n, 0, 5}, {m, Binomial[n+3, 3] -1, Binomial[n+4, 3] -2}]//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 >;
[(&+[Lucas(k)*A023533(n+2-k): k in [1..n+1]]): n in [0..50]]; // G. C. Greubel, Jul 16 2022
(SageMath)
def A023623(n, k): return sum(lucas_number2(k-binomial(j+3, 3), 1, -1) for j in (0..n))
flatten([[A023623(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
Sequence in context: A181408 A004979 A051788 * A023558 A170902 A000205
KEYWORD
nonn
STATUS
approved