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}] (* G. C. Greubel, Oct 27 2016 *)
(* Alternative: *)
LinearRecurrence[{0, 19, 0, -90}, {1, 2, 20, 38}, 25] (* G. C. Greubel, Oct 27 2016 *)

Prog

(PARI) a(n)=([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; -90, 0, 19, 0]^(n-1)*[1; 2; 20; 38])[1, 1] \\ Charles R Greathouse IV, May 29 2026

Crossrefs

Cf. A050250, A050685.

Sequence in context: A062133 A329729 A395714 * A073214 A293356 A269669

Adjacent sequences: A050681 A050682 A050683 * A050685 A050686 A050687

Keyword

nonn,base,easy,changed

Author

Patrick De Geest, Aug 15 1999

Extensions

More terms from David Wasserman, Feb 14 2002

Status

approved