A118004 a(n) = 9^n - 4^n.

0, 5, 65, 665, 6305, 58025, 527345, 4766585, 42981185, 387158345, 3485735825, 31376865305, 282412759265, 2541798719465, 22876524019505, 205890058352825, 1853015893884545, 16677164519797385, 150094566577522385, 1350851442795085145, 12157664359545301025, 109418984733465848105, 984770884591425188465

Offset: 0

Author

Eric W. Weisstein, Apr 09 2006

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Eric Weisstein's World of Mathematics, Cantor Square Fractal
• Index entries for linear recurrences with constant coefficients, signature (13,-36).

Crossrefs

Cf. A001047, A007689, A016153.

Programs

Magma

[9^n-4^n: n in [0..30]]; // G. C. Greubel, Nov 11 2024

Mathematica

Table[9^n-4^n,{n,0,30}] (* or *) LinearRecurrence[{13,-36},{0,5},30] (* Harvey P. Dale, May 11 2017 *)

PARI

a(n)=9^n-4^n \\ Charles R Greathouse IV, Oct 07 2015

SageMath

A118004=BinaryRecurrenceSequence(13,-36,0,5)
[A118004(n) for n in range(31)] # G. C. Greubel, Nov 11 2024

Formula

a(n) = 5*A016153(n).

a(n) = 13*a(n-1) - 36*a(n-2), n>=2. - Vincenzo Librandi, Mar 16 2011

G.f.: 5*x / ( (1-4*x)*(1-9*x) ). - R. J. Mathar, Mar 18 2011

From G. C. Greubel, Nov 11 2024: (Start)

a(n) = A001047(n)*A007689(n).

E.g.f.: 2*exp(13*x/2)*sinh(5*x/2). (End)

Extensions

More terms added by G. C. Greubel, Nov 11 2024