OFFSET
0,4
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..5000
Index entries for linear recurrences with constant coefficients, signature (-2,-3,-2,-1).
FORMULA
a(n) = Sum_{k=ceiling((n-1)/2)..n} (-1)^(k+1)*C(k+1,n-k)*(k*n-1))/(k+1).
a(3n+1) = 1, a(3n) = 1 - 3n, a(3n+2) = 3n. - Ralf Stephan, Mar 17 2014
MATHEMATICA
CoefficientList[Series[(x+1)*(3*x^2+2*x+1)/(x^2+x+1)^2, {x, 0, 50}], x] (* or *) LinearRecurrence[{-2, -3, -2, -1}, {1, 1, 0, -2}, 30] (* G. C. Greubel, May 26 2018 *)
PROG
(Maxima) a(n):=sum(((-1)^(k+1)*binomial(k+1, n-k)*(k*n-1))/(k+1), k, ceiling((n-1)/2), n);
(PARI) my(x='x+O('x^30)); Vec((x+1)*(3*x^2+2*x+1)/(x^2+x+1)^2) \\ G. C. Greubel, May 26 2018
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Vladimir Kruchinin, Mar 14 2014
STATUS
approved