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A192759
Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined below in Comments.
2
0, 1, 2, 4, 7, 12, 21, 35, 58, 95, 155, 253, 411, 667, 1081, 1751, 2836, 4591, 7431, 12026, 19461, 31492, 50958, 82455, 133418, 215878, 349302, 565186, 914494, 1479686, 2394186, 3873879, 6268072, 10141958, 16410037, 26552002, 42962047
OFFSET
0,3
COMMENTS
The titular polynomial is defined recursively by p(n,x)=x*(n-1,x)+floor((n+5)/5) for n>0, where p(0,x)=1. For discussions of polynomial reduction, see A192232 and A192744.
FORMULA
Conjecture: G.f.: -x / ( (x^2+x-1)*(x^4+x^3+x^2+x+1)*(x-1)^2 ), partial sums of A124502. - R. J. Mathar, May 04 2014
MATHEMATICA
p[0, n_] := 1; p[n_, x_] := x*p[n - 1, x] + Floor[(n + 5)/5] /; n > 0;
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}]
(* A124502 *)
u2 = Table[Coefficient[Part[t, n], x, 1], {n, 1, z}]
(* A192759 *)
CROSSREFS
Sequence in context: A100482 A301762 A003293 * A289249 A094974 A306306
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jul 09 2011
STATUS
approved