A094364 Expansion of (1-5x)/(1-10x-100x^2).

1, 5, 150, 2000, 35000, 550000, 9000000, 145000000, 2350000000, 38000000000, 615000000000, 9950000000000, 161000000000000, 2605000000000000, 42150000000000000, 682000000000000000, 11035000000000000000

Offset

0,2

Comments

2*a(n)/10^n = A000032(n). Fifth binomial transform of 1, 0, 125, 0, 15625, ...

Links

Table of n, a(n) for n=0..16.

Index entries for linear recurrences with constant coefficients, signature (10,100).

Formula

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

Mathematica

CoefficientList[Series[(1-5x)/(1-10x-100x^2), {x, 0, 30}], x] (* or *) LinearRecurrence[{10, 100}, {1, 5}, 30] (* Harvey P. Dale, Aug 27 2019 *)

Crossrefs

Cf. A000032 (Lucas numbers).

Sequence in context: A332716 A230666 A113560 * A232788 A324097 A082441

Adjacent sequences: A094361 A094362 A094363 * A094365 A094366 A094367

Keyword

easy,nonn

Author

Paul Barry, Apr 26 2004

Status

approved