A155872 a(n) = 10^n + 11^n.

2, 21, 221, 2331, 24641, 261051, 2771561, 29487171, 314358881, 3357947691, 35937424601, 385311670611, 4138428376721, 44522712143931, 479749833583241, 5177248169415651, 55949729863572161, 605447028499293771, 6559917313492231481, 71159090448414546291, 772749994932560009201

Offset: 0

Author

Avik Roy (avik_3.1416(AT)yahoo.co.in), Jan 29 2009

Keywords

• nonn
• easy

Comments

a(n) gives the combined total number of n digit numbers [preceding zeros allowed] in base 10 and 11.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..900
• Index entries for linear recurrences with constant coefficients, signature (21,-110).

Programs

Magma

[10^n+11^n: n in [0..30]]; // Vincenzo Librandi, Feb 06 2013

Mathematica

CoefficientList[Series[1/(1 - 10 x) + 1/(1 - 11 x), {x, 0, 30}], x] (* Vincenzo Librandi, Feb 06 2013 *)
LinearRecurrence[{21,-110},{2,21},20] (* Harvey P. Dale, Aug 27 2020 *)

Formula

G.f.: 1/(1-10*x) + 1/(1-11*x). - Vincenzo Librandi, Feb 06 2013

From Elmo R. Oliveira, Sep 12 2024: (Start)

E.g.f.: exp(10*x)*(exp(x) + 1).

a(n) = 21*a(n-1) - 110*a(n-2) for n > 1. (End)