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G.f.: (1 + 4*x - 5*x^2 + 10*x^3) / ((1 - x) * (1 - 10*x^2)).
a(n) = a(n-1) + 10*a(n-2) - 10*a(n-3). - Wesley Ivan Hurt, Aug 25 2022
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(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
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allocated for Ilya Gutkovskiy
Expansion of (1 + 4*x - 5*x^2 + 10*x^3) / ((1 - x) * (1 - 10*x^2)).
1, 5, 10, 60, 110, 610, 1110, 6110, 11110, 61110, 111110, 611110, 1111110, 6111110, 11111110, 61111110, 111111110, 611111110, 1111111110, 6111111110, 11111111110, 61111111110, 111111111110, 611111111110, 1111111111110, 6111111111110, 11111111111110, 61111111111110, 111111111111110
0,2
Number of odd palindromes <= 10^n.
Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PalindromicNumber.html">Palindromic Number</a>
<a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,10,-10).
nmax = 28; CoefficientList[Series[(1 + 4 x - 5 x^2 + 10 x^3) / ((1 - x) (1 - 10 x^2)), {x, 0, nmax}], x]
Join[{1}, LinearRecurrence[{1, 10, -10}, {5, 10, 60}, 28]]
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nonn,base,easy
Ilya Gutkovskiy, Oct 12 2019
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