A228569 Binomial transform of A006497.

2, 5, 19, 80, 343, 1475, 6346, 27305, 117487, 505520, 2175139, 9359135, 40270258, 173273885, 745558651, 3207971600, 13803182047, 59391995435, 255550431034, 1099576168865, 4731229551223, 20357419249520, 87593407593931, 376894780221095, 1621693678323682

Offset

0,1

Links

Michael De Vlieger, Table of n, a(n) for n = 0..1577

P. Bhadouria, D. Jhala, and B. Singh, Binomial Transforms of the k-Lucas Sequences and its Properties, The Journal of Mathematics and Computer Science (JMCS), Volume 8, Issue 1, Pages 81-92; sequence B_3.

Takao Komatsu, Asymmetric Circular Graph with Hosoya Index and Negative Continued Fractions, arXiv:2105.08277 [math.CO], 2021.

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

Formula

G.f.: (2-5*x)/(1-5*x+3*x^2).

a(n) = 2*A116415(n)-5*A116315(n-1) for n>0.

a(n) = ((5 + sqrt(13))/2)^n + ((5 - sqrt(13))/2)^n. - Taras Goy, Jun 02 2026

E.g.f.: 2*exp(5*x/2)*cosh(sqrt(13)*x/2). - Stefano Spezia, Jun 03 2026

Mathematica

LinearRecurrence[{5, -3}, {2, 5}, 30] (* Harvey P. Dale, Sep 09 2017 *)

Crossrefs

Cf. A006497, A116315, A116415.

Sequence in context: A277969 A058131 A222055 * A204328 A377785 A288911

Adjacent sequences: A228566 A228567 A228568 * A228570 A228571 A228572

Keyword

easy,nonn,changed

Author

R. J. Mathar, Nov 10 2013

Status

approved