%I #10 Aug 25 2022 08:58:40

%S 1,5,10,60,110,610,1110,6110,11110,61110,111110,611110,1111110,

%T 6111110,11111110,61111110,111111110,611111110,1111111110,6111111110,

%U 11111111110,61111111110,111111111110,611111111110,1111111111110,6111111111110,11111111111110,61111111111110,111111111111110

%N Expansion of (1 + 4*x - 5*x^2 + 10*x^3) / ((1 - x) * (1 - 10*x^2)).

%C Number of odd palindromes <= 10^n.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PalindromicNumber.html">Palindromic Number</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,10,-10).

%F G.f.: (1 + 4*x - 5*x^2 + 10*x^3) / ((1 - x) * (1 - 10*x^2)).

%F a(n) = a(n-1) + 10*a(n-2) - 10*a(n-3). - _Wesley Ivan Hurt_, Aug 25 2022

%t nmax = 28; CoefficientList[Series[(1 + 4 x - 5 x^2 + 10 x^3) / ((1 - x) (1 - 10 x^2)), {x, 0, nmax}], x]

%t Join[{1}, LinearRecurrence[{1, 10, -10}, {5, 10, 60}, 28]]

%o (PARI) Vec((1 + 4*x - 5*x^2 + 10*x^3) / ((1 - x) * (1 - 10*x^2)) + O(x^30)) \\ _Michel Marcus_, Oct 13 2019

%Y Cf. A002113, A029950, A050250, A070199, A328333.

%K nonn,base,easy

%O 0,2

%A _Ilya Gutkovskiy_, Oct 12 2019