A134250 Expansion of x*(4+9*x-7*x^2) / ((1-x)*(1+3*x-x^2)).

4, 1, 7, -14, 55, -173, 580, -1907, 6307, -20822, 68779, -227153, 750244, -2477879, 8183887, -27029534, 89272495, -294847013, 973813540, -3216287627, 10622676427, -35084316902, 115875627139, -382711198313, 1264009222084, -4174738864559, 13788225815767

Offset: 1

Author

Roger L. Bagula, Jan 14 2008

Keywords

• easy
• sign

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (-2,4,-1).

Crossrefs

Cf. A062709, A052548.

Programs

Maple

A134250 := proc(n)
        2-17*(-1)^n*A006190(n)+5*(-1)^n*A006190(n+1) ;
end proc:
seq(A134250(n),n=1..10) ; # R. J. Mathar, Dec 06 2011

Mathematica

LinearRecurrence[{-2,4,-1},{4,1,7},30] (* Harvey P. Dale, Aug 15 2015 *)
Rest@ CoefficientList[Series[x (4 + 9 x - 7 x^2)/((1 - x) (1 + 3 x - x^2)), {x, 0, 27}], x] (* Michael De Vlieger, May 16 2017 *)

PARI

Vec(x*(4+9*x-7*x^2)/((1-x)*(1+3*x-x^2)) + O(x^30)) \\ Colin Barker, May 16 2017

Formula

a(n) = 2-17*(-1)^n*A006190(n) +5*(-1)^n*A006190(n+1). - R. J. Mathar, Dec 06 2011

From Colin Barker, May 16 2017: (Start)

a(n) = 2 + (2^(-1-n)*((-3-sqrt(13))^n*(-19+5*sqrt(13)) + (-3+sqrt(13))^n*(19+5*sqrt(13)))) / sqrt(13).

a(n) = -2*a(n-1) + 4*a(n-2) - a(n-3) for n>3.

(End)