A050720 - OEIS

%I #32 Mar 12 2024 02:50:49

%S 0,0,9,9,171,171,2439,2439,30951,30951,368559,368559,4217031,4217031,

%T 46953279,46953279,512579511,512579511,5513215599,5513215599,

%U 58618940391,58618940391,617570463519,617570463519,6458134171671

%N Number of nonzero palindromes of length n containing the digit '0'.

%F G.f.: 9*x^3*(x+1) / ((3*x-1)*(3*x+1)*(10*x^2-1)). - _Colin Barker_, Feb 15 2013

%F For n > 1, a(n) = 9*10^(k-1) - 9^k, where k = ceiling(n/2). - _Jon E. Schoenfield_, Sep 14 2013

%e For length 3 we find nine numbers: 101, 202, ... 909, so a(3) = 9.

%t nzp[n_]:=Module[{k=Ceiling[n/2]},9*10^(k-1)-9^k]; Array[nzp,30] (* _Harvey P. Dale_, Jun 01 2019 *)

%Y Cf. A050683, A050686.

%K nonn,base

%O 1,3

%A _Patrick De Geest_, Aug 15 1999

%E More terms from Michael Lugo (mlugo(AT)thelabelguy.com), Dec 22 1999

%E Corrected by _T. D. Noe_, Nov 08 2006