A192802 Coefficient of x in the reduction of the polynomial (x+2)^n by x^3->x^2+x+1.

0, 1, 4, 13, 42, 143, 514, 1915, 7268, 27805, 106680, 409633, 1573086, 6040587, 23193782, 89051615, 341901032, 1312664601, 5039704492, 19348873781, 74285859698, 285204660583, 1094982340202, 4203950929347, 16140172668812

Offset

0,3

Comments

For discussions of polynomial reduction, see A192232 and A192744.

Links

Table of n, a(n) for n=0..24.

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*(3*x-1)/(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.)
LinearRecurrence[{7, -15, 11}, {0, 1, 4}, 30] (* Harvey P. Dale, Nov 05 2015 *)

Crossrefs

Cf. A192744, A192232, A192801, A192803.

Sequence in context: A070031 A082989 A267240 * A149425 A047144 A072307

Adjacent sequences: A192799 A192800 A192801 * A192803 A192804 A192805

Keyword

nonn,easy

Author

Clark Kimberling, Jul 10 2011

Extensions

Recurrence corrected by Colin Barker, Jul 27 2012

Status

approved