A232729 Number of n-digit numbers that yield an n-digit number after Reverse and Add.
4, 45, 405, 4095, 40500, 405450, 4050000, 40504500, 405000000, 4050045000, 40500000000, 405000450000, 4050000000000, 40500004500000, 405000000000000, 4050000045000000, 40500000000000000, 405000000450000000, 4050000000000000000, 40500000004500000000, 405000000000000000000
Offset: 1
Examples
There are 4 1-digit numbers (1,2,3,4) that yield a 1-digit number (2,4,6,8), so a(1)=4.
Links
- Robert Israel, Table of n, a(n) for n = 1..990
- Index entries for linear recurrences with constant coefficients, signature (10,10,-100).
Programs
-
PARI
Vec(x*(4+5*x-85*x^2-5*x^3)/((1-10*x)*(1-10*x^2)) + O(x^50)) \\ Colin Barker, Apr 22 2016
Formula
a(n) + A232730(n) = 9*10^(n-1).
a(1) = 4, a(3) = 405, a(2k+1) = 100*a(2k-1), k > 1.
a(2) = 45, a(4) = 4095, a(2k) = 110*a(2k-2) - 1000*a(2k-4), k > 2.
From Colin Barker, Apr 21 2016: (Start)
a(n) = 10*a(n-1)+10*a(n-2)-100*a(n-3) for n>4.
G.f.: x*(4+5*x-85*x^2-5*x^3) / ((1-10*x)*(1-10*x^2)). (End)
E.g.f.: (81*cosh(10*x) + 90*cosh(sqrt(10)*x) + 81*sinh(10*x) - 10*x - 171)/200. - Stefano Spezia, Oct 27 2022