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A192240 Constant term in the reduction of the polynomial (x+3)^n by x^2 -> x+1. 2
1, 3, 10, 37, 149, 636, 2813, 12695, 57922, 265809, 1223521, 5640748, 26026505, 120137307, 554669594, 2561176781, 11826871933, 54615158940, 252210521317, 1164706900879, 5378632571666, 24838652091993, 114705606355625, 529714071477452 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

See A192232.

LINKS

Table of n, a(n) for n=1..24.

FORMULA

Empirical G.f. and recurrence: x*(1-4*x)/(1-7*x+11*x^2). a(n)=7*a(n-1)-11*a(n-2). [Colin Barker, Feb 09 2012]

MATHEMATICA

q[x_] := x + 1;

p[n_, x_] := (x + 3)^n;

reductionRules = {x^y_?EvenQ -> q[x]^(y/2),

   x^y_?OddQ -> x q[x]^((y - 1)/2)};

t = Table[

   Last[Most[

     FixedPointList[Expand[#1 /. reductionRules] &, p[n, x]]]], {n, 0,

     30}];

Table[Coefficient[Part[t, n], x, 0], {n, 1, 30}]  (* A192240 *)

Table[Coefficient[Part[t, n], x, 1], {n, 1, 30}]  (* A099453 *)

(* by Peter J. C. Moses, Jun 26 2011 *)

CROSSREFS

Cf. A192232.

Sequence in context: A199874 A151058 A044048 * A231894 A086444 A064613

Adjacent sequences:  A192237 A192238 A192239 * A192241 A192242 A192243

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jun 26 2011

STATUS

approved

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Last modified February 19 19:30 EST 2020. Contains 332047 sequences. (Running on oeis4.)