%I #50 Oct 28 2021 06:29:44

%S 1,2,2,4,4,3,8,8,6,4,16,16,12,8,5,77,77,33,16,10,6,154,154,66,77,11,

%T 12,7,605,605,132,154,22,33,14,8,1111,1111,363,605,44,66,55,16,9,2222,

%U 2222,726,1111,88,132,110,77,18,10,4444,4444,1353,2222,176,363,121,154,99,11,11

%N Table T(n,r) of terms in the reverse and add sequences of positive integers n read by antidiagonals.

%H Alois P. Heinz, <a href="/A243238/b243238.txt">Antidiagonals n = 1..141, flattened</a>

%H <a href="/index/Res#RAA">Index entries for sequences related to Reverse and Add!</a>

%e T(5,6) = 88, since 88 is the 6th term in the reverse and add sequence of 5.

%e Table starts with:

%e 1 2 4 8 16 77 154 605 1111 2222

%e 2 4 8 16 77 154 605 1111 2222 4444

%e 3 6 12 33 66 132 363 726 1353 4884

%e 4 8 16 77 154 605 1111 2222 4444 8888

%e 5 10 11 22 44 88 176 847 1595 7546

%e 6 12 33 66 132 363 726 1353 4884 9768

%e 7 14 55 110 121 242 484 968 1837 9218

%e 8 16 77 154 605 1111 2222 4444 8888 17776

%e 9 18 99 198 1089 10890 20691 40293 79497 158994

%e 10 11 22 44 88 176 847 1595 7546 14003

%p T:= proc(n, r) option remember; `if`(r=1, n, (h-> h +(s->

%p parse(cat(s[-i]$i=1..length(s))))(""||h))(T(n, r-1)))

%p end:

%p seq(seq(T(n, 1+d-n), n=1..d), d=1..12); # _Alois P. Heinz_, Jun 18 2014

%t rad[n_] := n + FromDigits[Reverse[IntegerDigits[n]]];

%t T[n_, 1] := n; T[n_, k_] := T[n, k] = rad[T[n, k-1]];

%t Table[T[n-k+1, k], {n, 1, 12}, {k, n, 1, -1}] // Flatten (* _Jean-François Alcover_, Apr 08 2016 *)

%Y Rows n=1, 3, 5, 7, 9 give: A001127, A033648, A033649, A033650, A033651.

%Y Cf. A006960, A023108, A033670, A088753, A089694, A240510.

%Y Main diagonal gives A244058.

%K nonn,base,tabl

%O 1,2

%A _Felix Fröhlich_, Jun 12 2014