A257288 a(n) = 7*8^n-6*7^n.

1, 14, 154, 1526, 14266, 128534, 1129114, 9738806, 82851706, 697402454, 5821341274, 48265581686, 397988613946, 3266956634774, 26716987140634, 217805235562166, 1770927253556986, 14366815611873494, 116330307978911194, 940412945418752246, 7591696934462256826

Offset: 0

Author

M. F. Hasler, May 03 2015

Keywords

• nonn
• easy

Comments

First differences of 8^n-7^n = A016177.

a(n-1) is the number of numbers with n digits having the largest digit equal to 7. Note that this is independent of the base b > 7.

Equivalently, number of n-letter words over a 8-letter alphabet, which must not start with the last letter of the alphabet, and in which the first letter of the alphabet must appear.

Links

• Index entries for linear recurrences with constant coefficients, signature (15,-56).

Crossrefs

Cf. A016177.

Programs

Magma

[7*8^n-6*7^n: n in [0..20]]; // Vincenzo Librandi, May 04 2015

Mathematica

Table[7 8^n - 6 7^n, {n, 0, 30}] (* Vincenzo Librandi, May 04 2015 *)

PARI

a(n)=7*8^n-6*7^n

Formula

G.f.: (1-x)/((1-7*x)*(1-8*x)). - Vincenzo Librandi, May 04 2015

E.g.f.: exp(7*x)*(7*exp(x) - 6). - Stefano Spezia, Nov 15 2023