A107248 a(n) = 4*a(n-2) - 4*a(n-4) + 25*a(n-6).

1, 1, 1, 37, 37, 169, 169, 553, 553, 2461, 2461, 11857, 11857, 51409, 51409, 219733, 219733, 969721, 969721, 4285177, 4285177, 18755149, 18755149, 82122913, 82122913, 360600481, 360600481, 1582788997, 1582788997, 6941826889

Offset: 0

Author

Roger L. Bagula, Jun 08 2005

Keywords

• nonn
• easy
• less

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0, 4, 0, -4, 0, 25).

Crossrefs

Cf. A007493.

Programs

Magma

I:=[1,1,1,37,37,169]; [n le 6 select I[n] else 4*Self(n-2)-4*Self(n-4)+25*Self(n-6): n in [1..40]]; // Vincenzo Librandi, Feb 21 2018

Mathematica

CoefficientList[Series[-(1 + x - 3 x^2 + 33 x^3 + 37 x^4 + 25 x^5)/((5 x^3 - 2 x^2 + 1) (5 x^3 + 2 x^2 - 1)), {x, 0, 29}], x] (* Michael De Vlieger, Feb 20 2018 *)
LinearRecurrence[{0, 4, 0, -4, 0, 25}, {1, 1, 1, 37, 37, 169}, 30] (* Vincenzo Librandi, Feb 21 2018 *)

Formula

From R. J. Mathar, Jul 03 2009: (Start)

a(n) = 4*a(n-2) - 4*a(n-4) + 25*a(n-6).

G.f.: -(1+x-3*x^2+33*x^3+37*x^4+25*x^5)/((5*x^3-2*x^2+1)*(5*x^3+2*x^2-1)).

(End)

Extensions

Edited by N. J. A. Sloane, May 13 2006

New name using Mathar's recurrence from Joerg Arndt, Feb 20 2018