A163067 a(n) = 14*a(n-1) - 44*a(n-2) for n > 1; a(0) = 2, a(1) = 19.

2, 19, 178, 1656, 15352, 142064, 1313408, 12136896, 112126592, 1035748864, 9566914048, 88363846656, 816149635072, 7538085638144, 69622614990848, 643040841793536, 5939176725512192, 54854677118255104, 506641703733035008

Offset

0,1

Comments

Binomial transform of A163066. Inverse binomial transform of A163068.

Links

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

Index entries for linear recurrences with constant coefficients, signature (14,-44).

Formula

a(n) = ((2+sqrt(5))*(7+sqrt(5))^n+(2-sqrt(5))*(7-sqrt(5))^n)/2.

G.f.: (2-9*x)/(1-14*x+44*x^2).

Mathematica

CoefficientList[Series[(2-9*x)/(1-14*x+44*x^2), {x, 0, 50}], x] (* or *) LinearRecurrence[{14, -44}, {2, 19}, 30] (* G. C. Greubel, Dec 22 2017 *)

Prog

(Magma) [ n le 2 select 17*n-15 else 14*Self(n-1)-44*Self(n-2): n in [1..20] ];
(PARI) x='x+O('x^30); Vec((2-9*x)/(1-14*x+44*x^2)) \\ G. C. Greubel, Dec 22 2017

Crossrefs

Cf. A163066, A163068.

Sequence in context: A037574 A037742 A037637 * A221904 A124262 A140781

Adjacent sequences: A163064 A163065 A163066 * A163068 A163069 A163070

Keyword

nonn

Author

Klaus Brockhaus, Jul 20 2009

Status

approved