A099840 Expansion of (1-6*x)/(1-20*x^2).

1, -6, 20, -120, 400, -2400, 8000, -48000, 160000, -960000, 3200000, -19200000, 64000000, -384000000, 1280000000, -7680000000, 25600000000, -153600000000, 512000000000, -3072000000000, 10240000000000, -61440000000000, 204800000000000, -1228800000000000

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,20).

Formula

a(n) = (-2*sqrt(5))^n*(1/2 + 3*sqrt(5)/10) + (2*sqrt(5))^n*(1/2 - 3*sqrt(5)/10).

From G. C. Greubel, Apr 21 2023: (Start)

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

E.g.f.: cosh(2*sqrt(5)*x) - (3/sqrt(5))*sinh(2*sqrt(5)*x). (End)

Mathematica

LinearRecurrence[{0, 20}, {1, -6}, 41] (* G. C. Greubel, Apr 21 2023 *)
CoefficientList[Series[(1-6x)/(1-20x^2), {x, 0, 30}], x] (* Harvey P. Dale, Dec 02 2023 *)

Prog

(Magma) [n le 2 select 8-7*n else 20*Self(n-2): n in [1..41]]; // G. C. Greubel, Apr 21 2023
(SageMath)
def A099840(n): return 2*(2*sqrt(5))^(n-1)*(-3*(n%2) + sqrt(5)*((n+1)%2))
[A099840(n) for n in range(41)] # G. C. Greubel, Apr 21 2023

Crossrefs

Fifth binomial transform of A099839.

Sequence in context: A045470 A117998 A267855 * A223045 A245855 A074012

Adjacent sequences: A099837 A099838 A099839 * A099841 A099842 A099843

Keyword

easy,sign

Author

Paul Barry, Oct 27 2004

Status

approved