A050684 Number of nonzero palindromes < 10^n and containing at least one digit '1'.

1, 2, 20, 38, 290, 542, 3710, 6878, 44390, 81902, 509510, 937118, 5685590, 10434062, 62170310, 113906558, 669532790, 1225159022, 7125795110, 13026431198, 75132155990, 137237880782, 786189403910, 1435140927038

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0,19,0,-90).

Formula

a(2n) = 2*(10^n - 9^n); a(2n + 1) = 2*(10^n - 9^n) + 9*10^n - 8*9^n. - David Wasserman, Feb 14 2002

Example

Up to 10^2 we find two numbers 1 and 11.

Mathematica

Table[If[EvenQ[n], 2*(10^(n/2) - 9^(n/2)) , 2*(10^((n - 1)/2) - 9^((n - 1)/2)) + 9*10^((n - 1)/2) - 8*9^((n - 1)/2)], {n, 25}] (* or *) LinearRecurrence[{0, 19, 0, -90}, {1, 2, 20, 38}, 25] (* G. C. Greubel, Oct 27 2016 *)

Crossrefs

Cf. A050250, A050685.

Sequence in context: A298761 A062133 A329729 * A073214 A293356 A269669

Adjacent sequences: A050681 A050682 A050683 * A050685 A050686 A050687

Keyword

nonn,base

Author

Patrick De Geest, Aug 15 1999

Extensions

More terms from David Wasserman, Feb 14 2002

Status

approved