A167889 a(n) = (-7*3^n+(-3)^n+6*4^n) / 42.

0, 0, 1, 4, 25, 100, 481, 1924, 8425, 33700, 141361, 565444, 2320825, 9283300, 37664641, 150658564, 607417225, 2429668900, 9761722321, 39046889284, 156574977625, 626299910500, 2508686426401, 10034745705604, 40170363882025

Offset

0,4

Comments

This is the main sequence for the recurrence a(n) = 4*a(n-1) + 9*a(n-2) - 36*a(n-3) in the sense that the numerator of the g.f. contains only a power of x.

Links

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

Index entries for linear recurrences with constant coefficients, signature (4,9,-36).

Formula

a(n+1) - 4*a(n) = 0 if n even, = A001019((n-1)/2) if n odd.

G.f. x^2/( (3*x-1)*(3*x+1)*(4*x-1) ). - R. J. Mathar, Jul 04 2011

From G. C. Greubel, Jun 30 2016: (Start)

a(n) = 4*a(n-1) + 9*a(n-2) - 36*a(n-3).

E.g.f.: (1/42)*(exp(-3*x) - 7*exp(3*x) + 6*exp(4 x)). (End)

Mathematica

LinearRecurrence[{4, 9, -36}, {0, 0, 1}, 100] (* or *) Table[(-7*3^n + (-3)^n + 6*4^n)/42, {n, 0, 50}] (* G. C. Greubel, Jun 30 2016 *)

Prog

(Magma) [(-7*3^n+(-3)^n+6*4^n) / 42: n in [0..30]]; // Vincenzo Librandi, Jul 01 2016

Crossrefs

Sequence in context: A152215 A231175 A082044 * A329495 A042651 A225692

Adjacent sequences: A167886 A167887 A167888 * A167890 A167891 A167892

Keyword

nonn,easy

Author

Paul Curtz, Nov 14 2009

Extensions

More terms from Vincenzo Librandi, Apr 05 2010

Status

approved