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A328332 Expansion of (1 + 4*x - 5*x^2 + 10*x^3) / ((1 - x) * (1 - 10*x^2)).

%I A328332 #11 Feb 16 2025 08:33:58
%S A328332 1,5,10,60,110,610,1110,6110,11110,61110,111110,611110,1111110,
%T A328332 6111110,11111110,61111110,111111110,611111110,1111111110,6111111110,
%U A328332 11111111110,61111111110,111111111110,611111111110,1111111111110,6111111111110,11111111111110,61111111111110,111111111111110
%N A328332 Expansion of (1 + 4*x - 5*x^2 + 10*x^3) / ((1 - x) * (1 - 10*x^2)).
%C A328332 Number of odd palindromes <= 10^n.
%H A328332 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PalindromicNumber.html">Palindromic Number</a>
%H A328332 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,10,-10).
%F A328332 G.f.: (1 + 4*x - 5*x^2 + 10*x^3) / ((1 - x) * (1 - 10*x^2)).
%F A328332 a(n) = a(n-1) + 10*a(n-2) - 10*a(n-3). - _Wesley Ivan Hurt_, Aug 25 2022
%t A328332 nmax = 28; CoefficientList[Series[(1 + 4 x - 5 x^2 + 10 x^3) / ((1 - x) (1 - 10 x^2)), {x, 0, nmax}], x]
%t A328332 Join[{1}, LinearRecurrence[{1, 10, -10}, {5, 10, 60}, 28]]
%o A328332 (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 A328332 Cf. A002113, A029950, A050250, A070199, A328333.
%K A328332 nonn,base,easy
%O A328332 0,2
%A A328332 _Ilya Gutkovskiy_, Oct 12 2019