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A192380 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, 20, 60, 230, 776, 2792, 9720, 34410, 120780, 425788, 1497716, 5274190, 18562320, 65348560, 230024944, 809742418, 2850375060, 10033806180, 35320352940, 124333050422, 437670231064, 1540664252600, 5423363437800, 19091038878650, 67203259647836 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The polynomial p(n,x) is defined by ((x+d)^n-(x-d)^n)/(2d), where d=sqrt(x+2).  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..27.

Index entries for linear recurrences with constant coefficients, signature (2,6,-2,-1).

FORMULA

a(n) = 2*a(n-1)+6*a(n-2)-2*a(n-3)-a(n-4). G.f.: 2*x^2 / (x^4+2*x^3-6*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)=2+x+3x^2 -> 5+4x

p(3,x)=8x+4x^2+4x^3 -> 8+20x

p(4,x)=4+4x+21x^2+10x^3+5x^4 -> 45+60x.

From these, read

A192379=(1,0,5,8,45,...) and A192380=(0,2,4,20,60,...)

MATHEMATICA

(See A192379.)

CROSSREFS

Cf. A192232, A192379, A192381.

Sequence in context: A052004 A027741 A137697 * A009336 A274520 A238229

Adjacent sequences:  A192377 A192378 A192379 * A192381 A192382 A192383

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jun 29 2011

STATUS

approved

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Last modified February 19 15:01 EST 2018. Contains 299334 sequences. (Running on oeis4.)