A353582 a(n) = 2*a(n-1) + 2*a(n-3) + a(n-4) - 1, with a(0) = 0 = a(1), a(2) = 2, and a(3) = 3.

0, 0, 2, 3, 5, 13, 33, 78, 186, 450, 1088, 2625, 6335, 15295, 36927, 89148, 215220, 519588, 1254398, 3028383, 7311161, 17650705, 42612573, 102875850, 248364270, 599604390, 1447573052, 3494750493, 8437074035, 20368898563, 49174871163, 118718640888, 286612152936, 691942946760

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 (3,-2,2,-1,-1).

Formula

a(n) = (1/16)((4-s)*(1+s)^n + (4+s)*(1-s)^n - 8*sin(n*Pi/2) - 12*cos(n*Pi/2) + 4) where s = sqrt(2).

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

Crossrefs

Sequence in context: A175093 A342180 A345076 * A233515 A173268 A141179

Adjacent sequences: A353579 A353580 A353581 * A353583 A353584 A353585

Keyword

nonn,easy

Author

Paul K. Stockmeyer, May 04 2022

Status

approved