A034491 a(n) = 7^n + 1.

2, 8, 50, 344, 2402, 16808, 117650, 823544, 5764802, 40353608, 282475250, 1977326744, 13841287202, 96889010408, 678223072850, 4747561509944, 33232930569602, 232630513987208, 1628413597910450, 11398895185373144

Offset: 0

Author

N. J. A. Sloane

Keywords

• easy
• nonn

Links

• T. D. Noe, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (8,-7).

Crossrefs

Cf. A000051, A007689, A034472, A034474, A034494, A034524, A052539.

Cf. A062394, A062395, A062396, A062397, A063376, A063481.

Cf. A074600 - A074624, A178248, A228081.

Programs

Magma

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

Mathematica

7^Range[0,30] +1
LinearRecurrence[{8,-7},{2,8},20] (* Harvey P. Dale, Aug 18 2018 *)

PARI

a(n)=7^n+1 \\ Charles R Greathouse IV, Sep 24 2015

Sage

[sigma(7,n) for n in range(0,20)] # Zerinvary Lajos, Jun 04 2009

Formula

a(n) = 7*a(n-1) - 6.

a(n) = 8*a(n-1) - 7*a(n-2).

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

G.f.: 1/(1-x) + 1/(1-7*x).

E.g.f.: exp(x) + exp(7*x). (End)

a(n) = 2*A034494(n). - G. C. Greubel, Mar 11 2023