A192803 - OEIS

A192803

Coefficient of x^2 in the reduction of the polynomial (x+2)^n by x^3->x^2+x+1.

0, 0, 1, 7, 34, 144, 575, 2239, 8632, 33164, 127297, 488571, 1875346, 7199124, 27637959, 106107659, 407374592, 1564024808, 6004739025, 23053921567, 88510638482, 339817775144, 1304657986015, 5008956298247, 19230819824088, 73832632141076

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OFFSET

0,4

COMMENTS

For discussions of polynomial reduction, see A192232 and A192744.

LINKS

Table of n, a(n) for n=0..25.

J. Pan, Multiple Binomial Transforms and Families of Integer Sequences , J. Int. Seq. 13 (2010), 10.4.2, T^(2).

Index entries for linear recurrences with constant coefficients, signature (7,-15,11).

FORMULA

a(n) = 7*a(n-1)-15*a(n-2)+11*a(n-3).

G.f.: -x^2/(11*x^3-15*x^2+7*x-1). [Colin Barker, Jul 27 2012]

EXAMPLE

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

p(1,x)=1 -> 1

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

p(3,x)=x^2+4x+4 -> x^2+1

p(4,x)=x^3+6x^2+12x+8 -> x^2+4x+4

p(5,x)=x^4+8x^3+24x^2+32x+16 -> 7x^2+13*x+9, so that

A192798=(1,2,4,9,25,...), A192799=(0,1,4,13,42,...), A192800=(0,0,1,7,34,...).

MATHEMATICA

(See A192801.)

CROSSREFS

Cf. A192744, A192232, A192616, A192801, A192802.

Sequence in context: A094256 A094891 A306376 * A052161 A080960 A243414

Adjacent sequences: A192800 A192801 A192802 * A192804 A192805 A192806

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jul 10 2011

EXTENSIONS

Recurrence corrected by Colin Barker, Jul 27 2012

STATUS

approved

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