OFFSET
0,2
COMMENTS
First differences are 2, 2, 2, 8, 8, 8, 14, 14, 14, 20, 20, 20,... (triplicated A016933).
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..5000
Index entries for linear recurrences with constant coefficients, signature (2,-1,1,-2,1).
FORMULA
a(n) = 2*a(n-1) - a(n-2) + a(n-3) - 2*a(n-4) + a(n-5).
G.f.: (1 +x -x^3 +5*x^4)/( (1 +x +x^2)*(1 -x)^3 ).
E.g.f.: (1/3)*((7+3*x^2)*exp(x) - 4*exp(-x/2)*cos(sqrt(3)*x/2)). - G. C. Greubel, Aug 24 2017
MATHEMATICA
LinearRecurrence[{2, -1, 1, -2, 1}, {1, 3, 5, 7, 15}, 60] (* or *) CoefficientList[ Series[-(1+x+5x^4-x^3)/((1+x+x^2)(x-1)^3), {x, 0, 60}], x] (* Harvey P. Dale, Apr 20 2011 *)
PROG
(PARI) x='x+O('x^50); Vec((1+x-x^3+5*x^4)/((1+x+x^2)*(1-x)^3)) \\ G. C. Greubel, Aug 24 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Aug 07 2009
EXTENSIONS
Edited and extended by R. J. Mathar, Aug 12 2009
STATUS
approved