OFFSET
0,3
COMMENTS
LINKS
Index entries for linear recurrences with constant coefficients, signature (4,-5,1,2,-1).
FORMULA
a(n)=4*a(n-1)-5*a(n-2)+a(n-3)+2*a(n-4)-a(n-5).
G.f.: ( 1+7*x^2-4*x^3+x^4-4*x ) / ( (x^2+x-1)*(x-1)^3 ). - R. J. Mathar, May 04 2014
MATHEMATICA
q = x^2; s = x + 1; z = 40;
p[0, x] := 1;
p[n_, x_] := x*p[n - 1, x] + n (n^2 - 1)/6;
Table[Expand[p[n, x]], {n, 0, 7}]
reduce[{p1_, q_, s_, x_}] :=
FixedPoint[(s PolynomialQuotient @@ #1 +
PolynomialRemainder @@ #1 &)[{#1, q, x}] &, p1]
t = Table[reduce[{p[n, x], q, s, x}], {n, 0, z}];
u1 = Table[Coefficient[Part[t, n], x, 0], {n, 1, z}]
(* A193044 *)
u2 = Table[Coefficient[Part[t, n], x, 1], {n, 1, z}]
(* A193045 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jul 15 2011
STATUS
approved