%I #32 Mar 20 2017 12:53:55

%S 4,14,93,256,1793,4872,34107,92590,648154,1759313,12315269,33427272,

%T 233991155,635119194,4445835138,12067267861,84470877438,229278099157,

%U 1604946701532,4356283914175,30493987422124,82769394462323,579385761306789,1572618495070552

%N Number of distinct integers with n digits which are the image of integers by the function Reverse and Add!.

%C a(n) is the cardinality of the set of Image(Reverse and Add!) intersected with [10^(n-1), 10^n[. Here we suppose that the domain of the function Reverse and Add! is {1, 2, 3, ...}

%C There are 4, 50, 450, 4590, 45405,... (A232731) ways to obtain integers with n = 1,2,... digits as images under the function "Reverse and add!", but many result in the same image and are counted here only once. Example: 11+digrev(11) = 22 and 20+digrev(20)=22 contribute only once to the set of distinct images at n=2. - _R. J. Mathar_, Jun 17 2011

%H Hiroaki Yamanouchi, <a href="/A190481/b190481.txt">Table of n, a(n) for n = 1..100</a>

%F Empirical g.f.: x*(4 + 18*x + 23*x^2 - 29*x^3 - 58*x^4 - 34*x^5 - 81*x^6 - 45*x^7 - 32*x^8 - 9*x^9) / ((1 + x)*(1 - 19*x^2)*(1 - 2*x + x^2 - x^3)*(1 + 2*x + x^2 + x^3)). - _Colin Barker_, Mar 20 2017

%e Example: let RaA(x) be the function Reverse and Add!, then:

%e RaA(1)=2

%e RaA(2)=4

%e RaA(3)=6

%e RaA(4)=8

%e RaA(5)=10

%e RaA(6)=11, ...

%e So a(1) is the cardinal of {2,4,6,8}, which is 4:

%p A055642 := proc(n) max(1,1+ilog10(n)) ; end proc:

%p A056964 := proc(n) n+digrev(n) ; end proc:

%p A190481 := proc(n) local s,i,ra ; s := {} ; for i from 1 to 10^n do ra := A056964(i) ; if A055642( ra) = n then s := s union {ra} ; end if; end do: nops(s) ; end proc:

%p for n from 1 do print(n,A190481(n)) ; end do: # _R. J. Mathar_, Jun 17 2011

%Y Cf. A056964, A067030.

%K nonn,base

%O 1,1

%A _Aldo González Lorenzo_, May 25 2011

%E a(9)-a(10) from _Lars Blomberg_, Dec 01 2013

%E a(11)-a(24) from _Hiroaki Yamanouchi_, Sep 04 2014