OFFSET
0,2
COMMENTS
LINKS
Index entries for linear recurrences with constant coefficients, signature (7,-15,11).
FORMULA
a(n) = 7*a(n-1)-15*a(n-2)+11*a(n-3).
G.f.: -(5*x^2-5*x+1)/(11*x^3-15*x^2+7*x-1). [Colin Barker, Jul 27 2012]
EXAMPLE
MATHEMATICA
q = x^3; s = x^2 + x + 1; z = 40;
p[n_, x_] := (x + 2)^n;
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}] (* A192801 *)
u2 = Table[Coefficient[Part[t, n], x, 1], {n, 1, z}]
(* A192802 *)
u3 = Table[Coefficient[Part[t, n], x, 2], {n, 1, z}]
(* A192803 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jul 10 2011
EXTENSIONS
Recurrence corrected by Colin Barker, Jul 27 2012
STATUS
approved