A070252 - OEIS

%I #21 Jul 31 2025 22:03:29

%S 10,9,90,90,900,900,9000,9000,90000,90000,900000,900000,9000000,

%T 9000000,90000000,90000000,900000000,900000000,9000000000,9000000000,

%U 90000000000,90000000000,900000000000,900000000000,9000000000000

%N Number of n-digit palindromes.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,10).

%F From _Colin Barker_, Aug 19 2013: (Start)

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

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

%F E.g.f.: x + 9*(cosh(sqrt(10)*x) - 1 + sqrt(10)*sinh(sqrt(10)*x))/10. - _Stefano Spezia_, Jun 11 2022

%t LinearRecurrence[{0,10},{10,9,90},25] (* _Stefano Spezia_, Jun 11 2022 *)

%o (Python)

%o def A070252(n): return 10 if n==1 else 9*10**(n-1>>1) # _Chai Wah Wu_, Jul 30 2025

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

%Y Partial sums give A070199.

%K base,nonn,easy

%O 1,1

%A _Amarnath Murthy_, May 06 2002