A162562 a(n) = ((5+sqrt(3))*(1+sqrt(3))^n + (5-sqrt(3))*(1-sqrt(3))^n)/2.

5, 8, 26, 68, 188, 512, 1400, 3824, 10448, 28544, 77984, 213056, 582080, 1590272, 4344704, 11869952, 32429312, 88598528, 242055680, 661308416, 1806728192, 4936073216, 13485602816, 36843352064, 100657909760, 275002523648

Offset: 0

Author

Al Hakanson (hawkuu(AT)gmail.com), Jul 06 2009

Keywords

• nonn

Comments

Binomial transform of A162813. Inverse binomial transform of A162563.

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2, 2).

Crossrefs

Cf. A162813, A162563.

Programs

Magma

Z:=PolynomialRing(Integers()); N:=NumberField(x^2-3); S:=[ ((5+r)*(1+r)^n+(5-r)*(1-r)^n)/2: n in [0..25] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 14 2009

Mathematica

LinearRecurrence[{2,2},{5,8},30] (* Harvey P. Dale, Aug 17 2013 *)

Formula

a(n) = 2*a(n-1) + 2*a(n-2) for n > 1; a(0) = 5, a(1) = 8.

G.f.: (5-2*x)/(1-2*x-2*x^2).

Extensions

Edited and extended beyond a(5) by Klaus Brockhaus, Jul 14 2009