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A192756
Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined below in Comments.
2
0, 1, 6, 17, 38, 75, 138, 243, 416, 699, 1160, 1909, 3124, 5093, 8282, 13445, 21802, 35327, 57214, 92631, 149940, 242671, 392716, 635497, 1028328, 1663945, 2692398, 4356473, 7049006, 11405619, 18454770, 29860539, 48315464, 78176163
OFFSET
0,3
COMMENTS
The titular polynomial is defined recursively by p(n,x)=x*(n-1,x)+5n for n>0, where p(0,x)=1. For discussions of polynomial reduction, see A192232 and A192744.
FORMULA
Conjecture: G.f.: -x*(1+3*x+x^2) / ( (x^2+x-1)*(x-1)^2 ). a(n) = A001924(n)+3*A001924(n-1)+A001924(n-2). Partial sums of A166863. - 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] + 5 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}]
(* A166863 *)
u2 = Table[Coefficient[Part[t, n], x, 1], {n, 1, z}]
(* A192756 *)
CROSSREFS
Sequence in context: A132127 A023621 A000385 * A004799 A085278 A366104
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jul 09 2011
STATUS
approved