A162772 a(n) = ((2+sqrt(5))*(4+sqrt(5))^n + (2-sqrt(5))*(4-sqrt(5))^n)/2.

2, 13, 82, 513, 3202, 19973, 124562, 776793, 4844162, 30208573, 188382802, 1174768113, 7325934082, 45685023413, 284894912402, 1776624041673, 11079148296962, 69090321917293, 430851944071762, 2686822011483873

Offset

0,1

Comments

Binomial transform of A162771. Fourth binomial transform of A162963. Inverse binomial transform of A162773.

Links

Table of n, a(n) for n=0..19.

Index entries for linear recurrences with constant coefficients, signature (8, -11).

Formula

a(n) = 8*a(n-1) - 11*a(n-1) for n > 1; a(0) = 2, a(1) = 13.

G.f.: (2-3*x)/(1-8*x+11*x^2).

Prog

(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-5); S:=[ ((2+r)*(4+r)^n+(2-r)*(4-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 19 2009
(PARI) a(n)=([0, 1; -11, 8]^n*[2; 13])[1, 1] \\ Charles R Greathouse IV, May 28 2026

Crossrefs

Cf. A162771, A162963, A162773.

Sequence in context: A037634 A074581 A020059 * A317892 A079752 A156018

Adjacent sequences: A162769 A162770 A162771 * A162773 A162774 A162775

Keyword

nonn,easy

Author

Al Hakanson (hawkuu(AT)gmail.com), Jul 13 2009

Extensions

Edited and extended beyond a(5) by Klaus Brockhaus, Jul 19 2009

Status

approved