A162770 a(n) = ((2+sqrt(5))*(1+sqrt(5))^n + (2-sqrt(5))*(1-sqrt(5))^n)/2.

2, 7, 22, 72, 232, 752, 2432, 7872, 25472, 82432, 266752, 863232, 2793472, 9039872, 29253632, 94666752, 306348032, 991363072, 3208118272, 10381688832, 33595850752, 108718456832, 351820316672, 1138514460672, 3684310188032

Offset

0,1

Comments

Binomial transform of A162963. Inverse binomial transform of A001077 without initial 1.

Links

Michael De Vlieger, Table of n, a(n) for n = 0..1960

Silvana Ramaj, New Results on Cyclic Compositions and Multicompositions, Master's Thesis, Georgia Southern Univ., 2021. See p. 35.

Index entries for linear recurrences with constant coefficients, signature (2,4).

Formula

a(n) = 2*a(n-1) + 4*a(n-2) for n > 1; a(0) = 2, a(1) = 7.

G.f.: (2+3*x)/(1-2*x-4*x^2).

a(n) = 2^(n-1) * A000032(n+3). - Diego Rattaggi, Jun 24 2020

Mathematica

LinearRecurrence[{2, 4}, {2, 7}, 30] (* Harvey P. Dale, Jan 13 2015 *)

Prog

(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-5); S:=[ ((2+r)*(1+r)^n+(2-r)*(1-r)^n)/2: n in [0..24] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 19 2009

Crossrefs

Cf. A000032, A001077, A162963.

Sequence in context: A030186 A289592 A292230 * A116387 A337805 A294006

Adjacent sequences: A162767 A162768 A162769 * A162771 A162772 A162773

Keyword

nonn

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