A215502 a(n) = (1+sqrt(3))^n + (-2)^n + (1-sqrt(3))^n + 1.

4, 1, 13, 13, 73, 121, 481, 1009, 3361, 7969, 24193, 61249, 177025, 464257, 1307137, 3493633, 9699841, 26190337, 72173569, 195941377, 537802753, 1464342529, 4010582017, 10937266177, 29920862209, 81665925121, 223274237953, 609678999553, 1666309128193

Offset: 0

Author

Peter Luschny, Aug 13 2012

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,6,-2,-4).

Crossrefs

Cf. A051927, A215500, A215503.

Programs

Magma

[Round((1+Sqrt(3))^n + (-2)^n + (1-Sqrt(3))^n + 1): n in [0..30]]; // G. C. Greubel, Apr 23 2018

Maple

A215502 := n -> 1+(1+sqrt(3))^n+(-2)^n+(1-sqrt(3))^n;
seq(simplify(A215502(i)),i=0..28);

Mathematica

Simplify/@Table[(1+Sqrt[3])^n+(1-Sqrt[3])^n+1+(-2)^n,{n,0,30}] (* or *) LinearRecurrence[{1,6,-2,-4},{4,1,13,13},30] (* Harvey P. Dale, Mar 12 2013 *)

PARI

x='x+O('x^30); Vec((4-3*x-12*x^2+2*x^3)/((1-x)*(1+2*x)*(1-2*x-2*x^2))) \\ G. C. Greubel, Apr 23 2018

Formula

From Colin Barker, Aug 20 2012: (Start)

a(n) = a(n-1) +6*a(n-2) -2*a(n-3) -4*a(n-4).

G.f.: (4-3*x-12*x^2+2*x^3)/((1-x)*(1+2*x)*(1-2*x-2*x^2)). (End)