A027012 a(n) = T(2*n, n+1), T given by A027011.

1, 6, 47, 199, 661, 1954, 5442, 14696, 39065, 103025, 270655, 709716, 1859412, 4869594, 12750611, 33383659, 87401977, 228824086, 599072310, 1568395100, 4106115485, 10749954101, 28143749827, 73681298664, 192900149736, 505019154414, 1322157317687

Offset

1,2

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (6,-13,13,-6,1)

Formula

a(1)=1, a(n) = Lucas(2*n+6) - (6*n^2+17*n+18). - Ralf Stephan, May 05 2005

From Colin Barker, Feb 19 2016: (Start)

a(n) = -8 + (2^(-1-n)*((3-sqrt(5))^n*(-15+7*sqrt(5))+(3+sqrt(5))^n*(15+7*sqrt(5))))/sqrt(5) + 13*(1+n) - 6*(1+n)*(2+n) for n>1.

a(n) = 6*a(n-1)-13*a(n-2)+13*a(n-3)-6*a(n-4)+a(n-5) for n>6.

G.f.: x*(1+24*x^2-18*x^3+6*x^4-x^5) / ((1-x)^3*(1-3*x+x^2)).

(End)

Mathematica

Join[{1}, LinearRecurrence[{6, -13, 13, -6, 1}, {6, 47, 199, 661, 1954}, 30]] (* Harvey P. Dale, Nov 17 2013 *)

Prog

(PARI) Vec(x*(1+24*x^2-18*x^3+6*x^4-x^5)/((1-x)^3*(1-3*x+x^2)) + O(x^40)) \\ Colin Barker, Feb 19 2016

Crossrefs

Sequence in context: A184725 A232495 A267233 * A160609 A267203 A353098

Adjacent sequences: A027009 A027010 A027011 * A027013 A027014 A027015

Keyword

nonn,easy

Author

Clark Kimberling

Extensions

More terms from Harvey P. Dale, Nov 17 2013

Status

approved