A178348 a(n) = Sum_{k=0..n} 1100^k.

1, 1101, 1211101, 1332211101, 1465432211101, 1611975432211101, 1773172975432211101, 1950490272975432211101, 2145539300272975432211101, 2360093230300272975432211101, 2596102553330300272975432211101, 2855712808663330300272975432211101

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..328

Index entries for linear recurrences with constant coefficients, signature (1101,-1100).

Formula

a(n) = 1100*a(n-1) + 1.

Lim_{n -> infinity} a(n)/1100^n = 1100/1099.

From Colin Barker, Oct 02 2015: (Start)

a(n) = 1101*a(n-1) - 1100*a(n-2) for n>=2.

G.f.: 1 / ((x-1)*(1100*x-1)). (End)

Example

As overlapping Pascal triangles:
.....1
....1.1.0.1
...1.2.1.1.1.0.1
..1.3.3.2.2.1.1.1.0.1
.1.4.6.5.4.3.2.2.1.1.1.0.1

Mathematica

Table[Sum[1100^k, {k, 0, n}], {n, 0, 11}] (* Michael De Vlieger, Oct 02 2015 *)

Prog

(PARI) Vec(1/((x-1)*(1100*x-1)) + O(x^25)) \\ Colin Barker, Oct 02 2015
(PARI) vector(100, n, n--; sum(k=0, n, 1100^k)) \\ Altug Alkan, Oct 06 2015
(Magma) [(1/1099)*(1100^n-1): n in [0..20]]; // Vincenzo Librandi, Oct 07 2015

Crossrefs

Cf. A000931, A007318.

Sequence in context: A283172 A283253 A178407 * A359149 A250796 A271431

Adjacent sequences: A178345 A178346 A178347 * A178349 A178350 A178351

Keyword

nonn,easy

Author

Mark Dols, May 25 2010

Extensions

Offset corrected by Joerg Arndt, Oct 03 2015

Status

approved