OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,0,-8,6,6,-8,0,3,-1).
FORMULA
G.f.: (1 -2*x -x^2 +5*x^3 -x^4 -2*x^5 +x^6)/((1-x)*(1-x^2))^3.
a(n) = Sum_{k=0..floor(n/2)} ( 1 + C(k+1,2)*C(n-2k+1,2) ).
From Colin Barker, Sep 12 2016: (Start)
a(n) = (2895 + 945*(-1)^n + (1786-90*(-1)^n)*n - 30*(3+(-1)^n)*n^2 + 40*n^3 + 30*n^4 + 4*n^5)/3840.
a(n) = (2*n^5+15*n^4+20*n^3-60*n^2+848*n+1920)/1920 for n even.
a(n) = (2*n^5+15*n^4+20*n^3-30*n^2+938*n+975)/1920 for n odd. (End)
MATHEMATICA
LinearRecurrence[{3, 0, -8, 6, 6, -8, 0, 3, -1}, {1, 1, 2, 3, 6, 12, 23, 43, 74}, 25] (* G. C. Greubel, Sep 11 2016 *)
CoefficientList[Series[(1 - 2 x - x^2 + 5 x^3 - x^4 - 2 x^5 + x^6) / ((1 - x) (1 - x^2))^3, {x, 0, 50}], x] (* Vincenzo Librandi, Sep 12 2016 *)
PROG
(PARI) Vec((1-2*x-x^2+5*x^3-x^4-2*x^5+x^6) / ((1-x)^6*(1+x)^3) + O(x^60)) \\ Colin Barker, Sep 12 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Jan 07 2009
STATUS
approved