OFFSET
0,3
COMMENTS
The factor 2^n (i.e., |1/q|^n) is present to keep the values integer.
See also A232600 and references therein for integer values of q.
LINKS
Stanislav Sykora, Table of n, a(n) for n = 0..1000
S. Sykora, Finite and Infinite Sums of the Power Series (k^p)(x^k), DOI 10.3247/SL1Math06.002, Section V.
Index entries for linear recurrences with constant coefficients, signature (-1,3,5,2).
FORMULA
a(n) = ((-1)^n*(9*n^2+12*n+2) - 2^(n+1))/27.
G.f.: x*(-1+x)/( (1-2*x)*(1+x)^3 ). - R. J. Mathar, Nov 23 2014
E.g.f.: (1/27)*(-2*exp(2*x) + (2 -21*x +9*x^2)*exp(-x)). - G. C. Greubel, Mar 31 2021
a(n) = - a(n-1) + 3*a(n-2) + 5*a(n-3) + 2*a(n-4). - Wesley Ivan Hurt, Mar 31 2021
EXAMPLE
a(3) = 2^3 * [0^2/2^0 - 1^2/2^1 + 2^2/2^2 - 3^2/2^3] = -5.
MAPLE
A232603:= n-> ((-1)^n*(2+12*n+9*n^2) -2^(n+1))/27; seq(A232603(n), n=0..35); # G. C. Greubel, Mar 31 2021
MATHEMATICA
LinearRecurrence[{-1, 3, 5, 2}, {0, -1, 2, -5}, 35] (* G. C. Greubel, Mar 31 2021 *)
PROG
(PARI) a(n)=((-1)^n*(9*n^2+12*n+2)-2^(n+1))/27;
(Magma) [((-1)^n*(2+12*n+9*n^2) -2^(n+1))/27: n in [0..30]]; // G. C. Greubel, Mar 31 2021
(Sage) [((-1)^n*(2+12*n+9*n^2) -2^(n+1))/27 for n in (0..30)] # G. C. Greubel, Mar 31 2021
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Stanislav Sykora, Nov 27 2013
STATUS
approved