OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..5000
Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).
FORMULA
a(2n) = 6n+1 = A016921(n).
a(2n+1) = 12n+8 = A017617(n).
a(n) = 2*a(n-2)-a(n-4) = (3n+1)*(3-(-1)^n)/2.
From G. C. Greubel, Apr 26 2016: (Start)
O.g.f.: (1 + 8*x + 5*x^2 + 4*x^3)/((1 - x)^2*(1 + x)^2).
E.g.f.: (1/2)*(-1 + 3*x + (3+9*x)*exp(2*x))*exp(-x). (End)
MATHEMATICA
LinearRecurrence[{0, 2, 0, -1}, {1, 8, 7, 20}, 70] (* Harvey P. Dale, Aug 15 2012 *)
Table[If[OddQ@ #, #, 2 #] &[3 n + 1], {n, 0, 65}] (* or *)
CoefficientList[Series[(1 + 8 x + 5 x^2 + 4 x^3)/((1 - x)^2 (1 + x)^2), {x, 0, 65}], x] (* Michael De Vlieger, Apr 27 2016 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Oct 08 2009
STATUS
approved