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
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Harvey P. Dale, Nov 17 2013
STATUS
approved