A353581 a(n) = 2*a(n-1) + 2*a(n-3) + a(n-4), with a(0) = 0 = a(1), a(2) = 2, and a(3) = 1.

0, 0, 2, 1, 2, 8, 20, 45, 108, 264, 638, 1537, 3710, 8960, 21632, 52221, 126072, 304368, 734810, 1773985, 4282778, 10339544, 24961868, 60263277, 145488420, 351240120, 847968662, 2047177441, 4942323542, 11931824528, 28805972600, 69543769725, 167893512048, 405330793824

Offset

0,3

Links

Paul K. Stockmeyer, Table of n, a(n) for n = 0..1000

Andreas M. Hinz and Paul K. Stockmeyer, Precious Metal Sequences and Sierpinski-Type Graphs, J. Integer Seq., Vol 25 (2022), Article 22.4.8.

Index entries for linear recurrences with constant coefficients, signature (2,0,2,1).

Formula

a(n) = (1/8) ((5-3*s)*(1+s)^n + (5+3*s)*(1-s)^n + 2*sin(n*Pi/2) - 10*cos(n*Pi/2)) where s = sqrt(2).

G.f.: x^2*(2 - 3*x)/((1 + x^2)*(1 - 2*x - x^2)). - Stefano Spezia, May 04 2022

Crossrefs

Sequence in context: A282885 A242841 A143208 * A188664 A326572 A119419

Adjacent sequences: A353578 A353579 A353580 * A353582 A353583 A353584

Keyword

nonn,easy

Author

Paul K. Stockmeyer, May 04 2022

Status

approved