A238366 a(n) = 5*a(n-2) + 2, a(0) = 1, a(1) = 2.

1, 2, 7, 12, 37, 62, 187, 312, 937, 1562, 4687, 7812, 23437, 39062, 117187, 195312, 585937, 976562, 2929687, 4882812, 14648437, 24414062, 73242187, 122070312, 366210937, 610351562, 1831054687, 3051757812, 9155273437, 15258789062, 45776367187, 76293945312

Offset: 0

Author

Philippe Deléham, Feb 25 2014

Keywords

• easy
• nonn

Comments

Row sums of triangle in A152717.

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,5,-5).

Crossrefs

Cf. A057651, A125831, A152717, A198306.

Programs

Mathematica

LinearRecurrence[{1,5,-5},{1,2,7},40] (* Harvey P. Dale, Jul 18 2024 *)

Formula

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

a(n) = Sum_{k=0..n} A152717(n,k).

a(2*n) = A057651(n).

a(2*n+1) = A125831(n+1) = 2*A003463(n+1).

a(n) = a(n-1) + 5*a(n-2) - 5*a(n-3), a(0) = 1, a(1) = 2, a(2) = 7.

a(n) = A198306(n+1) for n > 1. - Georg Fischer, Oct 23 2018