A050686 Number of palindromes of length n and containing the digit 1 (or any other fixed nonzero digit).

1, 1, 18, 18, 252, 252, 3168, 3168, 37512, 37512, 427608, 427608, 4748472, 4748472, 51736248, 51736248, 555626232, 555626232, 5900636088, 5900636088, 62105724792, 62105724792, 648951523128, 648951523128, 6740563708152

Offset

1,3

Links

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

Formula

Empirical g.f.: -x*(x-1)*(x+1)^2 / ((3*x-1)*(3*x+1)*(10*x^2-1)). - Colin Barker, Feb 15 2013

From Sela Fried, Dec 10 2024: (Start)

The conjectured g.f is correct.

a(n) = 9*10^(n/2 - 1) - 8*9^(n/2 - 1) if n is even

a(n) = 9*10^((n - 1)/2) - 8*9^((n - 1)/2) if n is odd. (End)

Example

For length 3 we find 18 numbers: 101, 111, 121, 131, 141, 151, 161, 171, 181, 191, 212, 313, 414, 515, 616, 717, 818, 919.

Crossrefs

Cf. A050683, A050720.

Sequence in context: A298378 A299245 A352365 * A165839 A372457 A177014

Adjacent sequences: A050683 A050684 A050685 * A050687 A050688 A050689

Keyword

nonn,base

Author

Patrick De Geest, Aug 15 1999

Extensions

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

Status

approved