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A192384 Coefficient of x in the reduction by x^2->x+1 of the polynomial p(n,x) defined below in Comments. 3
0, 2, 4, 24, 72, 312, 1088, 4288, 15744, 60192, 224832, 851072, 3197056, 12062592, 45398016, 171104256, 644354048, 2427699712, 9144222720, 34448209920, 129761986560, 488821962752, 1841370087424, 6936475090944, 26129575084032 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Constant term of the reduction by x^2->x+1 of the polynomial p(n,x) defined below in Comments.

The polynomial p(n,x) is defined by ((x+d)^n-(x-d)^n)/(2d), where d=sqrt(x+3).  For an introduction to reductions of polynomials by substitutions such as x^2->x+1, see A192232.

LINKS

Table of n, a(n) for n=1..25.

Index entries for linear recurrences with constant coefficients, signature (2,8,-4,-4).

FORMULA

a(n) = 2*a(n-1)+8*a(n-2)-4*a(n-3)-4*a(n-4). G.f.: 2*x^2 / (4*x^4+4*x^3-8*x^2-2*x+1). [Colin Barker, Dec 09 2012]

EXAMPLE

The first five polynomials p(n,x) and their reductions are as follows:

p(0,x)=1 -> 1

p(1,x)=2x -> 2x

p(2,x)=3+x+3x^2 -> 6+4x

p(3,x)=12x+4x^2+4x^3 -> 8+24x

p(4,x)=9+6x+31x^2+10x^3+5x^4 -> 60+72x.

From these, read

A192383=(1,0,6,8,60,...) and A192384=(0,2,4,24,72,...)

MATHEMATICA

(See A192383.)

CROSSREFS

Cf. A192232, A192383, A192385=(1/2)A192384.

Sequence in context: A068506 A272640 A192513 * A119036 A192382 A232205

Adjacent sequences:  A192381 A192382 A192383 * A192385 A192386 A192387

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 30 2011

STATUS

approved

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Last modified November 12 05:52 EST 2019. Contains 329051 sequences. (Running on oeis4.)