A034524 a(n) = 11^n + 1.

2, 12, 122, 1332, 14642, 161052, 1771562, 19487172, 214358882, 2357947692, 25937424602, 285311670612, 3138428376722, 34522712143932, 379749833583242, 4177248169415652, 45949729863572162, 505447028499293772

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• T. D. Noe, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (12,-11).

Crossrefs

Sequences of the form m^n + 1: A000012 (m=0), A007395 (m=1), A000051 (m=2), A034472 (m=3), A052539 (m=4), A034474 (m=5), A062394 (m=6), A034491 (m=7), A062395 (m=8), A062396 (m=9), A062397 (m=10), this sequence (m=11), A178248 (m=12), A141012 (m=13), A228081 (m=64).

Cf. A001020.

Programs

Magma

[11^n +1: n in [0..30]]; // G. C. Greubel, Mar 11 2023

Mathematica

LinearRecurrence[{12,-11},{2,12},18] (* Ray Chandler, Aug 26 2015 *)
11^Range[0,30]+1 (* G. C. Greubel, Mar 11 2023 *)

PARI

a(n)=11^n+1 \\ Charles R Greathouse IV, Sep 24 2015

Sage

[sigma(11,n)for n in range(0,18)] # - Zerinvary Lajos, Jun 04 2009

Formula

From Mohammad K. Azarian, Jan 02 2009: (Start)

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

E.g.f.: exp(x) + exp(11*x). (End)

From G. C. Greubel, Mar 11 2023: (Start)

a(n) = 11*a(n-1) - 10.

a(n) = A001020(n) + 1. (End)