A328332 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

Offset: 0

Author

Ilya Gutkovskiy, Oct 12 2019

Keywords

• nonn
• base
• easy

Comments

Number of odd palindromes <= 10^n.

Links

• Eric Weisstein's World of Mathematics, Palindromic Number
• Index entries for linear recurrences with constant coefficients, signature (1,10,-10).

Crossrefs

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

Programs

Mathematica

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]]

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

Formula

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