OFFSET
0,3
COMMENTS
LINKS
Index entries for linear recurrences with constant coefficients, signature (3,-2,-1,1).
FORMULA
a(n) = 3*a(n-1)-2*a(n-2)-a(n-3)+a(n-4). G.f.: x*(3*x^2-3*x-1) / ((x-1)^2*(x^2+x-1)). [Colin Barker, Dec 08 2012]
MATHEMATICA
p[0, n_] := 1; p[n_, x_] := x*p[n - 1, x] + n + 4;
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}]
(* A022319 *)
u2 = Table[Coefficient[Part[t, n], x, 1], {n, 1, z}]
(* A192762 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jul 09 2011
STATUS
approved