A123362 a(0) = 1, a(1) = 1, a(n) = 6*a(n-1) + 5*a(n-2) for n > 1.

1, 1, 11, 71, 481, 3241, 21851, 147311, 993121, 6695281, 45137291, 304300151, 2051487361, 13830424921, 93239986331, 628592042591, 4237752187201, 28569473336161, 192605600952971, 1298480972398631, 8753913839156641

Offset: 0

Author

Philippe Deléham, Oct 12 2006

Keywords

• nonn
• easy

Comments

Hankel transform is [1, 10, 0, 0, 0, 0, 0, 0, 0, 0, ...]. - Philippe Deléham, Dec 04 2008

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Lucyna Trojnar-Spelina, Iwona Włoch, On Generalized Pell and Pell-Lucas Numbers, Iranian Journal of Science and Technology, Transactions A: Science (2019), 1-7.
• Index entries for linear recurrences with constant coefficients, signature (6,5).

Programs

Mathematica

LinearRecurrence[{6, 5}, {1, 1}, 50] (* G. C. Greubel, Oct 12 2017 *)

PARI

x='x+O('x^50); Vec((1-5*x)/(1 - 6*x - 5*x^2)) \\ G. C. Greubel, Oct 12 2017

Formula

a(n) = Sum_{k = 0..n} 5^(n - k)*A122542(n, k).

G.f.: (1 - 5*x)/(1 - 6*x - 5*x^2).