A135246 Shifted Pell recurrence: a(n) = 2*a(n-2) + a(n-4).

1, 3, 5, 7, 11, 17, 27, 41, 65, 99, 157, 239, 379, 577, 915, 1393, 2209, 3363, 5333, 8119, 12875, 19601, 31083, 47321, 75041, 114243, 181165, 275807, 437371, 665857, 1055907, 1607521, 2549185, 3880899, 6154277, 9369319, 14857739, 22619537, 35869755, 54608393, 86597249, 131836323, 209064253, 318281039, 504725755, 768398401, 1218515763, 1855077841, 2941757281, 4478554083

Offset: 0

Author

Paul Curtz, Feb 15 2008

Keywords

• nonn
• easy

Comments

Mix A048655(n) and A001333(n+2).

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,2,0,1).

Crossrefs

Cf. A001333, A048655, A109543.

Programs

Mathematica

LinearRecurrence[{0, 2, 0, 1}, {1, 3, 5, 7}, 25] (* G. C. Greubel, Oct 04 2016 *)

PARI

Vec((1 + 3*x + 3*x^2 + x^3)/(1 - 2*x^2 - x^4) + O(x^50)) \\ Michel Marcus, Oct 05 2016

Formula

G.f.: (1 + 3*x + 3*x^2 + x^3)/(1 - 2*x^2 - x^4). - G. C. Greubel, Oct 04 2016

a(n) = 2*a(n-2) + a(n-4). - Wesley Ivan Hurt, Dec 30 2023