A163473 a(n) = 14*a(n-1) - 46*a(n-2) for n > 1; a(0) = 3, a(1) = 24.

3, 24, 198, 1668, 14244, 122688, 1062408, 9230064, 80350128, 700318848, 6108357984, 53302344768, 465248359488, 4061569173504, 35460543892608, 309615432515328, 2703431036154624, 23605724610459648, 206122316883322368

Offset: 0

Author

Klaus Brockhaus, Aug 11 2009

Keywords

• nonn

Comments

Binomial transform of A163472. Inverse binomial transform of A163474.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (14,-46).

Crossrefs

Cf. A163472, A163474.

Programs

Magma

[ n le 2 select 21*n-18 else 14*Self(n-1)-46*Self(n-2): n in [1..19] ];

Mathematica

LinearRecurrence[{14, -46}, {3, 24}, 50] (* G. C. Greubel, Jul 26 2017 *)

PARI

x='x+O('x^50); Vec((3-18*x)/(1-14*x+46*x^2)) \\ G. C. Greubel, Jul 26 2017

Formula

a(n) = ((3+sqrt(3))*(7+sqrt(3))^n + (3-sqrt(3))*(7-sqrt(3))^n)/2.

G.f.: (3-18*x)/(1-14*x+46*x^2).

E.g.f.: exp(7*x)*( 3*cosh(sqrt(3)*x) + sqrt(3)*sinh(sqrt(3)*x) ). - G. C. Greubel, Jul 26 2017