A377728 Convolution of Leonardo numbers with Jacobsthal numbers.

0, 1, 2, 7, 16, 39, 86, 189, 402, 847, 1760, 3631, 7438, 15165, 30794, 62343, 125904, 253783, 510758, 1026685, 2061730, 4136991, 8295872, 16627167, 33311646, 66716029, 133582106, 267406999, 535206832, 1071049287, 2143127030, 4287918141, 8578528818, 17161414255

Offset

0,3

Links

Table of n, a(n) for n=0..33.

Prabha Sivaraman Nair, Convolution Identities of p-numbers, Math. Montis. (2024), pp. 26-43.

Index entries for linear recurrences with constant coefficients, signature (3,0,-5,1,2).

Formula

a(n) = Sum_{i=0..n} L(i)*J(n-i) where L = A001595 and J = A001045.

a(n) = (3*J(n+2) - 2*L(n+1) - 1)/2 where L = A001595 and J = A001045.

G.f.: -x*(x^2-x+1)/((x-1)*(2*x-1)*(x+1)*(x^2+x-1)). - Alois P. Heinz, Nov 05 2024

E.g.f.: 2*cosh(2*x) + sinh(x) + 2*sinh(2*x) - 2*exp(x/2)*(5*cosh(sqrt(5)*x/2) + 3*sqrt(5)*sinh(sqrt(5)*x/2))/5. - Stefano Spezia, Nov 06 2024

Mathematica

LinearRecurrence[{3, 0, -5, 1, 2}, {0, 1, 2, 7, 16}, 34] (* Amiram Eldar, Nov 07 2024 *)

Prog

(Python)
from sympy import fibonacci
def A377728(n): return 1-(fibonacci(n+2)<<2)+(m:=(4<<n)+(1 if n&1 else -1))-m%3>>1 # Chai Wah Wu, Nov 09 2024

Crossrefs

Cf. A001045, A001595.

Sequence in context: A260505 A042243 A293378 * A041887 A129441 A093971

Adjacent sequences: A377725 A377726 A377727 * A377729 A377730 A377731

Keyword

nonn,easy,changed

Author

Prabha Sivaramannair, Nov 05 2024

Status

approved