OFFSET
0,2
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
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
MATHEMATICA
Table[7 8^n - 6 7^n, {n, 0, 30}] (* Vincenzo Librandi, May 04 2015 *)
PROG
(PARI) a(n)=7*8^n-6*7^n
(Magma) [7*8^n-6*7^n: n in [0..20]]; // Vincenzo Librandi, May 04 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
M. F. Hasler, May 03 2015
STATUS
approved