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

Author

Amarnath Murthy, May 06 2002

Keywords

• base
• nonn
• easy

Links

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

Crossrefs

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

Partial sums give A070199.

Programs

Mathematica

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

Python

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

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