OFFSET
0,3
LINKS
Index entries for linear recurrences with constant coefficients, signature (5,-8,4,1,-1).
FORMULA
G.f.: x*(1 + x)/((1 - x)^3*(1 - 2*x - x^2)).
E.g.f.: (1/4)*exp(x)*(-2*(x*(x + 5) + 5) + 7*sqrt(2)*sinh(sqrt(2)*x) + 10*cosh(sqrt(2)*x)).
a(n) = 5*a(n-1) - 8*a(n-2) + 4*a(n-3) + a(n-4) - a(n-5).
a(n) = (1/8)*(-4*(n*(n + 4) + 5) + (10 - 7*sqrt(2))*(1 - sqrt(2))^n + (10 + 7*sqrt(2))*(1 + sqrt(2))^n).
Lim_{n->infinity} a(n + 1)/a(n) = 1 + sqrt(2) = A014176.
MATHEMATICA
RecurrenceTable[{a[0] == 0, a[1] == 1, a[n] == 2 a[n - 1] + a[n - 2] + n^2}, a, {n, 31}]
LinearRecurrence[{5, -8, 4, 1, -1}, {0, 1, 6, 22, 66}, 32]
PROG
(PARI) x='x+O('x^99); concat(0, Vec(x*(1+x)/((1-x)^3*(1-2*x-x^2)))) \\ Altug Alkan, Apr 06 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ilya Gutkovskiy, Apr 06 2016
STATUS
approved