OFFSET
0,2
COMMENTS
FORMULA
Conjecture: G.f.: ( 1+5*x-2*x^2 ) / ( (x-1)*(x^2+x-1) ). a(n) = A000071(n+3)+5*A000071(n+2) -2*A000071(n+1) and first differences in A022136. - R. J. Mathar, May 04 2014
MATHEMATICA
q = x^2; s = x + 1; z = 40;
p[0, n_] := 1; p[n_, x_] := x*p[n - 1, x] + 4 n + 3;
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}](* A192752 *)
u2 = Table[Coefficient[Part[t, n], x, 1], {n, 1, z}](* A192753 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jul 09 2011
STATUS
approved