A070252 Number of n-digit palindromes.

10, 9, 90, 90, 900, 900, 9000, 9000, 90000, 90000, 900000, 900000, 9000000, 9000000, 90000000, 90000000, 900000000, 900000000, 9000000000, 9000000000, 90000000000, 90000000000, 900000000000, 900000000000, 9000000000000

Offset

1,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,10).

Formula

From Colin Barker, Aug 19 2013: (Start)

a(n) = 10*a(n-2) for n>3.

G.f.: x*(10*x^2-9*x-10) / (10*x^2-1). (End)

E.g.f.: x + 9*(cosh(sqrt(10)*x) - 1 + sqrt(10)*sinh(sqrt(10)*x))/10. - Stefano Spezia, Jun 11 2022

Mathematica

LinearRecurrence[{0, 10}, {10, 9, 90}, 25] (* Stefano Spezia, Jun 11 2022 *)

Prog

(Python)
def A070252(n): return 10 if n==1 else 9*10**(n-1>>1) # Chai Wah Wu, Jul 30 2025

Crossrefs

A variant of A050683, which is the principal entry for this sequence. Cf. A016115.

Partial sums give A070199.

Sequence in context: A241285 A052196 A243035 * A038311 A244960 A378564

Adjacent sequences: A070249 A070250 A070251 * A070253 A070254 A070255

Keyword

base,nonn,easy

Author

Amarnath Murthy, May 06 2002

Status

approved