A162559 a(n) = ((4+sqrt(3))*(1+sqrt(3))^n + (4-sqrt(3))*(1-sqrt(3))^n)/2.

4, 7, 22, 58, 160, 436, 1192, 3256, 8896, 24304, 66400, 181408, 495616, 1354048, 3699328, 10106752, 27612160, 75437824, 206099968, 563075584, 1538351104, 4202853376, 11482408960, 31370524672, 85705867264, 234152783872, 639717302272, 1747740172288, 4774914949120

Offset

0,1

Comments

Binomial transform of A162766. Inverse binomial transform of A077236.

Links

Table of n, a(n) for n=0..28.

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

Formula

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

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

Maple

seq((1/2)*simplify((4+sqrt(3))*(1+sqrt(3))^n+(4-sqrt(3))*(1-sqrt(3))^n), n = 0 .. 27); # Emeric Deutsch, Jul 16 2009

Mathematica

LinearRecurrence[{2, 2}, {4, 7}, 30] (* Harvey P. Dale, Sep 21 2018 *)

Prog

(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-3); S:=[ ((4+r)*(1+r)^n+(4-r)*(1-r)^n)/2: n in [0..25] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 13 2009

Crossrefs

Cf. A162766, A077236.

Sequence in context: A100098 A127361 A128533 * A126094 A073114 A083830

Adjacent sequences: A162556 A162557 A162558 * A162560 A162561 A162562

Keyword

nonn

Author

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

Extensions

Edited by Klaus Brockhaus, Paolo P. Lava and Emeric Deutsch, Jul 13 2009

Two different extensions were received. This version was rechecked by N. J. A. Sloane, Jul 19 2009

Status

approved