OFFSET
0,2
COMMENTS
LINKS
Carauleanu Marc, Table of n, a(n) for n = 0..2222
Ilya Gutkovskiy, Illustration
Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).
FORMULA
O.g.f.: (1 + 2*x - 2*x^3 + x^4)/((1 - x)^3*(1 + x)^2).
E.g.f.: ((-3 - 2*x)*exp(-x) + (11 + 12*x + 2*x^2)*exp(x))/8
a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n > 4.
a(n) = (2*n*(n + (-1)^n + 5) - 3*(-1)^n + 11)/8.
MATHEMATICA
LinearRecurrence[{1, 2, -2, -1, 1}, {1, 3, 5, 7, 11}, 66]
Table[(2 n (n + (-1)^n + 5) - 3 (-1)^n + 11)/8, {n, 0, 65}]
PROG
(PARI) Vec((1+2*x-2*x^3+x^4)/((1-x)^3*(1+x)^2) + O(x^99)) \\ Altug Alkan, Aug 27 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ilya Gutkovskiy, Aug 27 2016
STATUS
approved