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

Author

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

Keywords

• nonn

Comments

Binomial transform of A162766. Inverse binomial transform of A077236.

Links

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

Crossrefs

Cf. A162766, A077236.

Programs

Magma

Z:=PolynomialRing(Integers()); N:=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

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 *)

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).

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