A097178 Expansion of (1+10*x-101*x^2-900*x^3)/((1-100*x^2)*(1-101*x^2)).

1, 10, 100, 1110, 10000, 122110, 1000000, 13333110, 100000000, 1446644110, 10000000000, 156111055110, 1000000000000, 16767216566110, 100000000000000, 1793488873177110, 10000000000000000, 191142376190888110

Offset

0,2

Comments

Partial sums are A097177.

Links

G. C. Greubel, Table of n, a(n) for n = 0..980

Index entries for linear recurrences with constant coefficients, signature (0,201,0,-10100).

Formula

a(n) = (55/sqrt(101))*( (sqrt(101))^n - (-sqrt(101))^n ) + 10^n * (11*(-1)^n-9)/2.

a(n) = 201*a(n-2) - 10100*a(n-4).

Maple

seq(coeff(series((1+10*x-101*x^2-900*x^3)/((1-100*x^2)*(1-101*x^2)), x, n+1), x, n), n = 0 ..20); # G. C. Greubel, Sep 17 2019

Mathematica

CoefficientList[Series[(1+10x-101x^2-900x^3)/((1-100x^2)(1-101x^2)), {x, 0, 30}], x] (* Wesley Ivan Hurt, Jan 13 2017 *)
LinearRecurrence[{0, 201, 0, -10100}, {1, 10, 100, 1110}, 20] (* Harvey P. Dale, Mar 03 2018 *)

Prog

(PARI) my(x='x+O('x^20)); Vec((1+10*x-101*x^2-900*x^3)/((1-100*x^2)*(1-101*x^2))) \\ G. C. Greubel, Sep 17 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+10*x-101*x^2-900*x^3)/((1-100*x^2)*(1-101*x^2)) )); // G. C. Greubel, Sep 17 2019
(Sage)
def A097178_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P((1+10*x-101*x^2-900*x^3)/((1-100*x^2)*(1-101*x^2))).list()
A097178_list(20) # G. C. Greubel, Sep 17 2019
(GAP) a:=[1, 10, 100, 1110];; for n in [5..20] do a[n]:=201*a[n-2] - 10100*a[n-4]; od; a; # G. C. Greubel, Sep 17 2019

Crossrefs

Sequence in context: A164832 A144822 A199763 * A283288 A283377 A283352

Adjacent sequences: A097175 A097176 A097177 * A097179 A097180 A097181

Keyword

easy,nonn

Author

Paul Barry, Jul 30 2004

Status

approved