A135345 a(n) = 3*a(n-1) + 4*a(n-2) - a(n-3) + 3*a(n-4) + 4*a(n-5).

1, 4, 13, 51, 204, 819, 3277, 13108, 52429, 209715, 838860, 3355443, 13421773, 53687092, 214748365, 858993459, 3435973836, 13743895347, 54975581389, 219902325556, 879609302221, 3518437208883, 14073748835532, 56294995342131, 225179981368525, 900719925474100, 3602879701896397, 14411518807585587

Offset: 0

Author

Paul Curtz, Dec 06 2007

Keywords

• nonn
• easy

Comments

Companion to A135343.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,4,-1,3,4).

Crossrefs

Cf. A135343.

Programs

Mathematica

LinearRecurrence[{3,4,-1,3,4},{1,4,13,51,204}, 25] (* G. C. Greubel, Oct 10 2016 *)

PARI

Vec((1-3*x^2)/((1+x)*(1-4*x)*(1-x+x^2)) + O(x^30)) \\ Colin Barker, Oct 11 2016

Formula

4*a(n) - a(n+1) = hexaperiodic 0, 3, 1, 0, -3, -1.

a(n) = (4^(n+1)/5)-(2/15)*(-1)^n+(1/3)*cos(Pi*n/3)+(sqrt(3)/3)*cos(Pi*n/3). - Richard Choulet, Jan 04 2008

G.f.: ( -2*(3 + sqrt(3)) + (3 + 7*sqrt(3))*x + (9 + 5*sqrt(3))*x^2 -

4*(3 + sqrt(3))*x^3)/( 6*(-1 + 4*x - x^3 + 4*x^4) ). - G. C. Greubel, Oct 10 2016

G.f.: (1-3*x^2) / ((1+x)*(1-4*x)*(1-x+x^2)). - Colin Barker, Oct 11 2016

Extensions

Removed incorrect formula, Joerg Arndt, Oct 11 2016