A091105 Expansion of (1-5x+40x^2)/((1-5x)(1+5x)).

1, -5, 65, -125, 1625, -3125, 40625, -78125, 1015625, -1953125, 25390625, -48828125, 634765625, -1220703125, 15869140625, -30517578125, 396728515625, -762939453125, 9918212890625, -19073486328125, 247955322265625, -476837158203125, 6198883056640625

Offset

0,2

Comments

a(0)=1, a(2n-1)=-k^(2n-1), a(2n)=(3k-2)k^(2n-1), k=5; G.f.: (1-kx+2(k-1)kx^2)/((1-kx)(1+kx)), k=5.

Links

Table of n, a(n) for n=0..22.

Index entries for linear recurrences with constant coefficients, signature (0,25)

Formula

a(n)=4*5^n/5+9(-5)^n/5-8*0^n/5

a(0)=1, a(1)=-5, a(2)=65, a(n)=25*a(n-2) From Harvey P. Dale, Jul 15 2012

Mathematica

CoefficientList[Series[(1-5x+40x^2)/((1-5x)(1+5x)), {x, 0, 40}], x] (* or *) Join[{1}, LinearRecurrence[{0, 25}, {-5, 65}, 30]] (* Harvey P. Dale, Jul 15 2012 *)

Crossrefs

Sequence in context: A220557 A266962 A126955 * A234335 A071902 A211412

Adjacent sequences: A091102 A091103 A091104 * A091106 A091107 A091108

Keyword

easy,sign

Author

Paul Barry, Dec 22 2003

Status

approved