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A232729
Number of n-digit numbers that yield an n-digit number after Reverse and Add.
3
4, 45, 405, 4095, 40500, 405450, 4050000, 40504500, 405000000, 4050045000, 40500000000, 405000450000, 4050000000000, 40500004500000, 405000000000000, 4050000045000000, 40500000000000000, 405000000450000000, 4050000000000000000, 40500000004500000000, 405000000000000000000
OFFSET
1,1
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
EXAMPLE
There are 4 1-digit numbers (1,2,3,4) that yield a 1-digit number (2,4,6,8), so a(1)=4.
PROG
(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
CROSSREFS
Sequence in context: A122910 A343904 A117644 * A055602 A346629 A073565
KEYWORD
nonn,base,easy
AUTHOR
Lars Blomberg, Nov 29 2013
STATUS
approved