A133592 a(n) = 2*a(n-1)+6*a(n-2) for n>=3, a(0)=1, a(1)=2, a(2)=8.

1, 2, 8, 28, 104, 376, 1376, 5008, 18272, 66592, 242816, 885184, 3227264, 11765632, 42894848, 156383488, 570136064, 2078573056, 7577962496, 27627363328, 100722501632, 367209183232, 1338753376256, 4880761851904, 17794043961344

Offset: 0

Author

Philippe Deléham, Dec 31 2007

Keywords

• easy
• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (2,6).

Crossrefs

Cf. A083099, A122950.

Programs

Maple

A133592 := proc(n)
        option remember;
        if n <=1 then
                n+1;
        elif n = 2 then
                8;
        else
                2*procname(n-1)+6*procname(n-2) ;
        fi ;
end proc: # R. J. Mathar, Jul 15 2017

Mathematica

Join[{1}, LinearRecurrence[{2, 6}, {2, 8}, 24]] (* Jean-François Alcover, Jul 01 2023 *)

Formula

G.f.: (1-2*x^2)/(1-2*x-6*x^2).

a(n) = Sum_{k=0..n} A122950(n,k)*2^k .

a(n) = ((7+2*sqrt(7))/21)*(1+sqrt(7))^n+((7-2*sqrt(7))/21)*(1-sqrt(7))^n for n=>1. [Richard Choulet, Nov 19 2008]

a(n) = A083099(n+1) - 2*A083099(n-1). - R. J. Mathar, Jun 20 2015

Extensions

a(16) corrected by R. J. Mathar, Jun 20 2015