A257289 a(n) = 8*9^n - 7*8^n.

1, 16, 200, 2248, 23816, 243016, 2416520, 23583688, 226933256, 2159839816, 20378082440, 190918934728, 1778399954696, 16486635929416, 152228014061960, 1400838452135368, 12853836673840136, 117654854901535816, 1074656292809619080, 9798007424852945608

Offset: 0

Author

M. F. Hasler, May 03 2015

Keywords

• nonn
• easy

Comments

First differences of 9^n - 8^n = A016185.

a(n-1) is the number of numbers with n digits having the largest digit equal to 8. Note that this is independent of the base b > 8.

Equivalently, number of n-letter words over a 9-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 (17,-72).

Crossrefs

Cf. A016185.

See also A000225, A027649, A255463, A257285, A257286, A257287, A257288, and A088924.

Programs

Magma

[8*9^n-7*8^n: n in [0..20]]; // Vincenzo Librandi, May 04 2015

Mathematica

Table[8 9^n - 7 8^n, {n, 0, 20}] (* Vincenzo Librandi, May 04 2015 *)
LinearRecurrence[{17,-72},{1,16},30] (* Harvey P. Dale, May 26 2019 *)

PARI

a(n)=8*9^n-7*8^n

Sage

[8*9^n-7*8^n for n in (0..20)] # Bruno Berselli, May 04 2015

Formula

G.f.: (1-x)/((1-8*x)*(1-9*x)). - Vincenzo Librandi, May 04 2015

E.g.f.: exp(8*x)*(8*exp(x) - 7). - Stefano Spezia, Nov 15 2023