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A192762 Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined below in Comments. 5
0, 1, 6, 13, 26, 47, 82, 139, 232, 383, 628, 1025, 1668, 2709, 4394, 7121, 11534, 18675, 30230, 48927, 79180, 128131, 207336, 335493, 542856, 878377, 1421262, 2299669, 3720962, 6020663, 9741658, 15762355, 25504048, 41266439, 66770524 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The titular polynomial is defined recursively by p(n,x)=x*(n-1,x)+n+4 for n>0, where p(0,x)=1.  For discussions of polynomial reduction, see A192232 and A192744.

LINKS

Table of n, a(n) for n=0..34.

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

Cf. A192744, A192232, A022319 (first differences).

Sequence in context: A162432 A117072 A081395 * A268721 A183337 A301687

Adjacent sequences:  A192759 A192760 A192761 * A192763 A192764 A192765

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jul 09 2011

STATUS

approved

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Last modified July 5 17:29 EDT 2020. Contains 335473 sequences. (Running on oeis4.)