A023623 Convolution of Lucas numbers and A023533.

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

Author

Clark Kimberling

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..4700

Crossrefs

Cf. A000032, A023533.

Programs

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

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 *)

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

Formula

a(n) = Sum_{j=1..n+1} LucasL(j) * A023533(n-j+1). - G. C. Greubel, Jul 16 2022