A178396 a(1)=1, a(n) = a(n-1)*1000 + 11^(n-1) for n>=2.

1, 1011, 1011121, 1011122331, 1011122345641, 1011122345802051, 1011122345803822561, 1011122345803842048171, 1011122345803842262529881, 1011122345803842264887828691, 1011122345803842264913766115601, 1011122345803842264914051427271611

Offset

1,2

Comments

Numerators of fractions in partial sums of Sum_{n>=0} 11^n/1000^(n+1) converging to fraction 1/989 or Sum_{n>=0} 10^n/999^(n+1) whose alternating sum converges to fraction 1/1009 [= alternating sum_9^n/1000^(n+1)].

Links

Colin Barker, Table of n, a(n) for n = 1..334

Index entries for linear recurrences with constant coefficients, signature (1011,-11000).

Formula

From Colin Barker, Oct 02 2015: (Start)

a(n) = 1011*a(n-1) - 11000*a(n-2) for n>2.

G.f.: x / ((11*x-1)*(1000*x-1)).

(End)

Example

As overlapping Pascal triangles starting a new triangle to the left of each row skipping one place:
....................1
...............1.0.1.1
..........1.0.1.1.1.2.1
.....1.0.1.1.1.2.2.3.3.1
1.0.1.1.1.2.2.3.4.5.6.4.1

Prog

(PARI) Vec(x/((11*x-1)*(1000*x-1)) + O(x^40)) \\ Colin Barker, Oct 02 2015

Crossrefs

Cf. A000931, A007318.

Sequence in context: A185881 A115769 A267613 * A178349 A291962 A094946

Adjacent sequences: A178393 A178394 A178395 * A178397 A178398 A178399

Keyword

nonn,easy

Author

Mark Dols, May 27 2010

Extensions

Definition adapted to offset by Georg Fischer, Jun 19 2021

Status

approved