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

Author

R. J. Mathar, Nov 10 2013

Keywords

• easy
• nonn

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).

Programs

Mathematica

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

Formula

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

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