OFFSET
0,2
COMMENTS
First differences of 6^n - 5^n = A005062.
a(n-1) is the number of numbers with n digits having the largest digit equal to 5. Or, equivalently, number of n-letter words over a 6-letter alphabet {a,b,c,d,e,f}, which must not start with the first letter of the alphabet, and in which the last letter of the alphabet must appear.
LINKS
FORMULA
a(n) = 11 a(n-1) - 30 a(n-2).
G.f.: (1-x)/((1-5*x)*(1-6*x)). - Vincenzo Librandi, May 04 2015
E.g.f.: exp(5*x)*(5*exp(x) - 4). - Stefano Spezia, Nov 15 2023
MATHEMATICA
Table[5 6^n - 4 5^n, {n, 0, 30}] (* Vincenzo Librandi, May 04 2015 *)
PROG
(PARI) a(n)=5*6^n-4*5^n
(Magma) [5*6^n-4*5^n: n in [0..20]]; // Vincenzo Librandi, May 04 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
M. F. Hasler, May 03 2015
STATUS
approved