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

1,3

Links

Table of n, a(n) for n=1..25.

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

Example

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

Mathematica

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

Crossrefs

Cf. A050683, A050686.

Sequence in context: A092548 A121389 A065242 * A262860 A335026 A353182

Adjacent sequences: A050717 A050718 A050719 * A050721 A050722 A050723

Keyword

nonn,base

Author

Patrick De Geest, Aug 15 1999

Extensions

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

Corrected by T. D. Noe, Nov 08 2006

Status

approved