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A377728
Convolution of Leonardo numbers with Jacobsthal numbers.
1
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
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
Sequence in context: A260505 A042243 A293378 * A041887 A129441 A093971
KEYWORD
nonn,easy
AUTHOR
STATUS
approved