A103461 a(n) = (-10)^n + 1 - 0^n.

1, -9, 101, -999, 10001, -99999, 1000001, -9999999, 100000001, -999999999, 10000000001, -99999999999, 1000000000001, -9999999999999, 100000000000001, -999999999999999, 10000000000000001, -99999999999999999, 1000000000000000001, -9999999999999999999

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..900

Index entries for linear recurrences with constant coefficients, signature (-9,10).

Formula

G.f.: (1+10*x^2)/((1-x)*(1+10*x)).

a(n) = Sum_{k=0..n} binomial(n,k)*0^(k*(n-k))*(-10)^k.

E.g.f.: -1 + exp(x) + exp(-10*x). - G. C. Greubel, Jun 26 2021

Mathematica

Join[{1, -9}, Table[{10^(n-1)+1, -(10^n-1)}, {n, 3, 21, 2}]]//Flatten (* Harvey P. Dale, Apr 23 2019 *)
Table[(-10)^n +1 -Boole[n==0], {n, 0, 40}] (* G. C. Greubel, Jun 26 2021 *)

Prog

(Magma) [1] cat [(-10)^n +1: n in [1..40]]; // G. C. Greubel, Jun 26 2021
(Sage) [1]+[(-10)^n +1 for n in (1..40)] # G. C. Greubel, Jun 26 2021

Crossrefs

Sequence in context: A287039 A360348 A174509 * A101563 A269732 A007133

Adjacent sequences: A103458 A103459 A103460 * A103462 A103463 A103464

Keyword

easy,sign

Author

Paul Barry, Feb 07 2005

Status

approved