A050720 Number of nonzero palindromes of length n containing the digit '0'.
0, 0, 9, 9, 171, 171, 2439, 2439, 30951, 30951, 368559, 368559, 4217031, 4217031, 46953279, 46953279, 512579511, 512579511, 5513215599, 5513215599, 58618940391, 58618940391, 617570463519, 617570463519, 6458134171671
Offset: 1
Examples
For length 3 we find nine numbers: 101, 202, ... 909, so a(3) = 9.
Programs
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Mathematica
nzp[n_]:=Module[{k=Ceiling[n/2]},9*10^(k-1)-9^k]; Array[nzp,30] (* Harvey P. Dale, Jun 01 2019 *)
Formula
G.f.: 9*x^3*(x+1) / ((3*x-1)*(3*x+1)*(10*x^2-1)). - Colin Barker, Feb 15 2013
For n > 1, a(n) = 9*10^(k-1) - 9^k, where k = ceiling(n/2). - Jon E. Schoenfield, Sep 14 2013
Extensions
More terms from Michael Lugo (mlugo(AT)thelabelguy.com), Dec 22 1999
Corrected by T. D. Noe, Nov 08 2006