A169601 a(n) = (10^n - 1)^2 + 2.

2, 83, 9803, 998003, 99980003, 9999800003, 999998000003, 99999980000003, 9999999800000003, 999999998000000003, 99999999980000000003, 9999999999800000000003, 999999999998000000000003, 99999999999980000000000003, 9999999999999800000000000003, 999999999999998000000000000003

Offset

0,1

Links

Table of n, a(n) for n=0..15.

Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).

Formula

G.f.: -(2810*x^2-139*x+2)/((x-1)*(100*x-1)*(10*x-1)).

From Elmo R. Oliveira, Jul 08 2025: (Start)

E.g.f.: exp(x)*(3 - 2*exp(9*x) + exp(99*x)).

a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3). (End)

Mathematica

(10^Range[0, 20]-1)^2+2 (* Harvey P. Dale, Jan 08 2019 *)

Prog

(PARI) for(n=0, 20, print1((10^n-1)^2+2", "))
(PARI) my(x='x+O('x^16)); Vec((2810*x^2-139*x+2)/(-1000*x^3+1110*x^2-111*x+1)) \\ Elmo R. Oliveira, Jul 08 2025

Crossrefs

Sequence in context: A232770 A317724 A099373 * A367900 A205643 A215263

Adjacent sequences: A169598 A169599 A169600 * A169602 A169603 A169604

Keyword

nonn,easy

Author

Jason Earls, Dec 03 2009

Extensions

More terms from Elmo R. Oliveira, Jul 08 2025

Status

approved