OFFSET
0,2
COMMENTS
a(n) is the number of strings of n+1 decimal digits having an odd number of 0's. For 2 digits these are for example the 18 strings 01, 02, 03, ..., 09, 10, 20, 30, ..., 90. - Geoffrey Critzer, Jan 24 2011
LINKS
FORMULA
a(n) = 8*a(n-1) + 10^(n-1). - Geoffrey Critzer, Jan 24 2011
E.g.f.: exp(9*x)*sinh(x). - Geoffrey Critzer, Jan 24 2011
A060531(n) = a(n) - 9*a(n-1). - R. J. Mathar_, Jan 27 2011
a(n) = 10*a(n-1) + 8^n, a(0)=1. - Vincenzo Librandi, Feb 09 2011
a(n) = 18*a(n-1) - 80*a(n-2), a(0)=1, a(1)=18. - Vincenzo Librandi, Feb 09 2011
MATHEMATICA
Range[0, 20]! CoefficientList[Series[Exp[9 x] Sinh[x], {x, 0, 20}], x]
Join[{a=1, b=18}, Table[c=18*b-80*a; a=b; b=c, {n, 40}]] (* Vladimir Joseph Stephan Orlovsky, Feb 09 2011 *)
LinearRecurrence[{18, -80}, {1, 18}, 30] (* Harvey P. Dale, Aug 26 2019 *)
PROG
(PARI) Vec(1/((1-8*x)*(1-10*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 24 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved