A128415 Expansion of (1-4x^2)/(1+3x+4x^2).

1, -3, 1, 9, -31, 57, -47, -87, 449, -999, 1201, 393, -5983, 16377, -25199, 10089, 70529, -251943, 473713, -413367, -654751, 3617721, -8234159, 10231593, 2241857, -47651943, 133988401, -211357431, 98118689

Offset: 0

Author

Paul Barry, Mar 02 2007

Keywords

• easy
• sign

Comments

Row sums of number triangle A128414.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-3,-4).

Programs

Mathematica

CoefficientList[Series[(1 - 4 x^2) / (1 + 3 x + 4 x^2), {x, 0, 40}], x] (* Vincenzo Librandi, Jul 20 2013 *)
LinearRecurrence[{-3,-4},{1,-3,1},40] (* Harvey P. Dale, Sep 24 2022 *)

Formula

For n>0, a(n) = (1/r)^n + (1/s)^n, with r = (-3-i*sqrt(7))/8 and s = (-3+i*sqrt(7))/8 the roots of 4x^2+3x+1. - Ralf Stephan, Jul 20 2013

a(n) = -3*a(n-1) - 4*a(n-2) for n > 2. - Harry Richman, May 05 2020