A087213 Expansion of (1+x-4*x^2) / ((1+x)*(1-4*x^2)).

1, 0, 0, 4, -4, 20, -20, 84, -84, 340, -340, 1364, -1364, 5460, -5460, 21844, -21844, 87380, -87380, 349524, -349524, 1398100, -1398100, 5592404, -5592404, 22369620, -22369620, 89478484, -89478484, 357913940, -357913940, 1431655764, -1431655764, 5726623060

Offset

0,4

Comments

Binomial transform is A046717 (with extra leading 1).

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (-1,4,4).

Formula

a(2*n+1) = A002450(n) = A001045(2*n).

a(2*n+2) = -A002450(n) = -A001045(2*n).

a(n) = 2^n/6 - (-2)^n/2 + 4*(-1)^n/3.

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

Mathematica

CoefficientList[Series[(1 + x - 4 x^2)/((1 + x) (1 - 4 x^2)), {x, 0, 33}], x] (* or *) {1, 0}~Join~LinearRecurrence[{-1, 4, 4}, {0, 4, -4}, 32] (* Michael De Vlieger, Mar 17 2017 *)

Prog

(PARI) Vec((1 + x - 4*x^2) / ((1 + x)*(1 - 2*x)*(1 + 2*x)) + O(x^40)) \\ Colin Barker, Mar 17 2017

Crossrefs

Sequence in context: A264528 A035413 A261568 * A117857 A165559 A180967

Adjacent sequences: A087210 A087211 A087212 * A087214 A087215 A087216

Keyword

easy,sign

Author

Paul Barry, Aug 26 2003

Status

approved