A114553 a(n) = 25*a(n-2) + 48*a(n-3) with a(0) = 0, a(1) = a(2) = 1.

0, 1, 1, 25, 73, 673, 3025, 20329, 107929, 653425, 3674017, 21516217, 123214825, 714258241, 4113149041, 23770767625, 137113121593, 791700344593, 4568824885825, 26373938451289, 152222238686089, 878652055801825

Offset

0,4

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,25,48).

Formula

a(n) = w(n)((1)) where w(n) = M*w(n-1), w(0) = {0, 1, 1}, and M = {{0, 1, 0}, {0, 0, 1}, {48, 25, 0}}.

From Colin Barker, Sep 23 2012: (Start)

a(n) = 25*a(n-2) + 48*a(n-3).

G.f.: x*(1+x)/((1+3*x)*(1-3*x-16*x^2)). (End)

a(n) = (4*i)^(n-1)*(4*i*ChebyshevU(n, -3*I/8) - 5*ChebyshevU(n-1, -3*I/8)) - (-3)^n. - G. C. Greubel, Jul 07 2021

Mathematica

M = {{0, 1, 0}, {0, 0, 1}, {48, 25, 0}}; w[0] = {0, 1, 1};
w[n_]:= w[n]= M.w[n - 1];
Table[w[n][[1]], {n, 0, 30}]
LinearRecurrence[{0, 25, 48}, {0, 1, 1}, 30] (* Harvey P. Dale, Mar 26 2013 *)

Prog

(Magma) I:=[0, 1, 1]; [n le 3 select I[n] else 25*Self(n-2) + 48*Self(n-3): n in [1..31]]; // G. C. Greubel, Jul 07 2021
(Sage)
def a(n, q): return 0 if (n==0) else 1 if (n<3) else q^2*a(n-2, q) + 2*(q^2-1)*a(n-3, q)
[a(n, 5) for n in (0..30)] # G. C. Greubel, Jul 07 2021

Crossrefs

Sequence in context: A069190 A124718 A126379 * A098439 A318643 A044163

Adjacent sequences: A114550 A114551 A114552 * A114554 A114555 A114556

Keyword

nonn,easy

Author

Roger L. Bagula, Feb 15 2006

Extensions

New name and edited by G. C. Greubel, Jul 07 2021

Status

approved