OFFSET
1,1
COMMENTS
Essentially the same as A001019 = powers of 9.
Also number of n-digit positive integers with no identical adjacent digits. Hence the numerator (with A052268 as denominator) of the probability that an n-digit positive integer has this property (e.g., 9/9, 81/90, 729/900, ..., where A100062(n)/A052268(n) reduces to A001019(n-1)/A011557(n-1)). - Rick L. Shepherd, Jun 08 2008
LINKS
Stanislav Sykora, Table of n, a(n) for n = 1..666; previous Table by Rick L. Shepherd went up to n=30.
Tanya Khovanova, Recursive Sequences
Eric Weisstein's World of Mathematics, Evil Number
Index entries for linear recurrences with constant coefficients, signature (9).
FORMULA
a(n) = 9^n. - Max Alekseyev, Mar 03 2007
From Philippe Deléham, Nov 23 2008: (Start)
a(n) = 9*a(n-1), n>1; a(1)=9.
G.f.: 9x/(1-9x). (End)
a(n) = A001019(n) for n>0. - Wesley Ivan Hurt, Apr 18 2016
EXAMPLE
1/9, 10/81, 100/729, 1000/6561, 10000/59049, ...
MAPLE
MATHEMATICA
9^Range[20] (* Harvey P. Dale, Dec 25 2012 *)
PROG
(PARI) \\ The 'old' approach, using the generating function:
s = Vec(Ser((1-x^9)/(x^10-10*x+9), x, 666));
a = vector(#s, n, denominator(s[n])) \\ Stanislav Sykora, Apr 16 2016
(Magma) [9^n : n in [1..30]]; // Wesley Ivan Hurt, Apr 18 2016
CROSSREFS
KEYWORD
nonn,base,frac
AUTHOR
Eric W. Weisstein, Nov 01 2004
EXTENSIONS
More terms from Rick L. Shepherd, Jun 08 2008
STATUS
approved