A232729 - OEIS

%I #28 Oct 27 2022 10:21:23

%S 4,45,405,4095,40500,405450,4050000,40504500,405000000,4050045000,

%T 40500000000,405000450000,4050000000000,40500004500000,

%U 405000000000000,4050000045000000,40500000000000000,405000000450000000,4050000000000000000,40500000004500000000,405000000000000000000

%N Number of n-digit numbers that yield an n-digit number after Reverse and Add.

%H Robert Israel, <a href="/A232729/b232729.txt">Table of n, a(n) for n = 1..990</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (10,10,-100).

%F a(n) + A232730(n) = 9*10^(n-1).

%F a(1) = 4, a(3) = 405, a(2k+1) = 100*a(2k-1), k > 1.

%F a(2) = 45, a(4) = 4095, a(2k) = 110*a(2k-2) - 1000*a(2k-4), k > 2.

%F From _Colin Barker_, Apr 21 2016: (Start)

%F a(n) = 10*a(n-1)+10*a(n-2)-100*a(n-3) for n>4.

%F G.f.: x*(4+5*x-85*x^2-5*x^3) / ((1-10*x)*(1-10*x^2)). (End)

%F 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

%e There are 4 1-digit numbers (1,2,3,4) that yield a 1-digit number (2,4,6,8), so a(1)=4.

%o (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

%Y Cf. A232730, A232731.

%K nonn,base,easy

%O 1,1

%A _Lars Blomberg_, Nov 29 2013