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%I #29 Aug 26 2019 10:43:04
%S 1,18,244,2952,33616,368928,3951424,41611392,432891136,4463129088,
%T 45705032704,465640261632,4725122093056,47800976744448,
%U 482407813955584,4859262511644672,48874100093157376,490992800745259008
%N Expansion of 1/((1-8x)(1-10x)).
%C 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
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (18,-80).
%F a(n) = 5*10^n - 4*8^n = A081203(n+1). Binomial transform of A081035. - _R. J. Mathar_, Sep 18 2008
%F a(n) = 8*a(n-1) + 10^(n-1). - _Geoffrey Critzer_, Jan 24 2011
%F E.g.f.: exp(9*x)*sinh(x). - _Geoffrey Critzer_, Jan 24 2011
%F A060531(n) = a(n) - 9*a(n-1). - R. J. Mathar_, Jan 27 2011
%F a(n) = 10*a(n-1) + 8^n, a(0)=1. - _Vincenzo Librandi_, Feb 09 2011
%F a(n) = 18*a(n-1) - 80*a(n-2), a(0)=1, a(1)=18. - _Vincenzo Librandi_, Feb 09 2011
%t Range[0, 20]! CoefficientList[Series[Exp[9 x] Sinh[x], {x, 0, 20}], x]
%t Join[{a=1,b=18},Table[c=18*b-80*a;a=b;b=c,{n,40}]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 09 2011 *)
%t LinearRecurrence[{18,-80},{1,18},30] (* _Harvey P. Dale_, Aug 26 2019 *)
%o (PARI) Vec(1/((1-8*x)*(1-10*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 24 2012
%Y Cf. A060531.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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