A016186 Expansion of 1/((1-8x)(1-10x)).

1, 18, 244, 2952, 33616, 368928, 3951424, 41611392, 432891136, 4463129088, 45705032704, 465640261632, 4725122093056, 47800976744448, 482407813955584, 4859262511644672, 48874100093157376, 490992800745259008

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

Table of n, a(n) for n=0..17.

Index entries for linear recurrences with constant coefficients, signature (18,-80).

Formula

a(n) = 5*10^n - 4*8^n = A081203(n+1). Binomial transform of A081035. - R. J. Mathar, Sep 18 2008

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

Cf. A060531.

Sequence in context: A053540 A080601 A333298 * A081203 A016294 A153593

Adjacent sequences: A016183 A016184 A016185 * A016187 A016188 A016189

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved