A093835 a(n) = n * Jacobsthal(n).

0, 1, 2, 9, 20, 55, 126, 301, 680, 1539, 3410, 7513, 16380, 35503, 76454, 163845, 349520, 742747, 1572858, 3320497, 6990500, 14680071, 30758222, 64312669, 134217720, 279620275, 581610146, 1207959561, 2505397580, 5189752159, 10737418230, 22190664373, 45812984480

Offset

0,3

Comments

Convolution of Jacobsthal numbers A001045 and modified Jacobsthal-Lucas numbers (in A014551, change the leading 2 to a 1).

Links

Table of n, a(n) for n=0..32.

Index entries for linear recurrences with constant coefficients, signature (2,3,-4,-4).

Formula

G.f.: x*(1+2*x^2)/(1-x-2*x^2)^2.

a(n) = n*2^n/3 - n*(-1)^n/3.

a(n) = n*A001045(n). - R. J. Mathar, May 07 2019

E.g.f.: x * (exp(-x) + 2*exp(2*x)) / 3. - Amiram Eldar, Feb 20 2026

Mathematica

LinearRecurrence[{2, 3, -4, -4}, {0, 1, 2, 9}, 30] (* Harvey P. Dale, Jun 17 2017 *)

Crossrefs

Cf. A001045, A014551, A023607.

Sequence in context: A272211 A259035 A394934 * A264294 A280295 A041007

Adjacent sequences: A093832 A093833 A093834 * A093836 A093837 A093838

Keyword

nonn,easy

Author

Paul Barry, Apr 20 2004

Status

approved