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A128415 - OEIS
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A128415
Expansion of (1-4x^2)/(1+3x+4x^2).
4
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
0,2
COMMENTS
Row sums of number triangle A128414.
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
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 *)
CROSSREFS
Sequence in context: A273464 A105951 A038202 * A227795 A090479 A355559
KEYWORD
easy,sign
AUTHOR
Paul Barry, Mar 02 2007
STATUS
approved