A103458 a(n) = 7^n + 1 - 0^n.

1, 8, 50, 344, 2402, 16808, 117650, 823544, 5764802, 40353608, 282475250, 1977326744, 13841287202, 96889010408, 678223072850, 4747561509944, 33232930569602, 232630513987208, 1628413597910450, 11398895185373144

Offset: 0

Author

Paul Barry, Feb 07 2005

Keywords

• easy
• nonn

Comments

a(n)^3 is palindromic in base 7 (1_7, 1331_7, 1030301_7, 1003003001_7, ...).

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Patrick De Geest, World!Of Numbers
• Index entries for linear recurrences with constant coefficients, signature (8,-7).

Crossrefs

Cf. A034491, A046233.

Programs

Magma

[1] cat [7^n + 1: n in [1..30]]; // G. C. Greubel, Jun 22 2021

Mathematica

Table[7^n +1 -Boole[n==0], {n,0,30}] (* G. C. Greubel, Jun 22 2021 *)

Sage

[1]+[7^n + 1 for n in (1..30)] # G. C. Greubel, Jun 22 2021

Formula

G.f.: (1-7*x^2)/((1-x)*(1-7*x)).

a(n) = Sum_{k=0..n} binomial(n, k)*0^(k(n-k))*7^k.

a(n) = A034491(n), n > 0. - R. J. Mathar, Aug 28 2008

a(n) = 7*a(n-1) - 6, with a(1)=8. - Vincenzo Librandi, Dec 29 2010

E.g.f.: -1 + exp(x) + exp(7*x). - G. C. Greubel, Jun 22 2021