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%I #12 Feb 18 2018 02:50:16
%S 1,2,2,4,1,4,7,3,3,7,3,6,1,6,3,8,10,4,4,10,8,14,5,8,1,8,5,14,21,11,13,
%T 5,5,13,11,21,13,4,7,10,1,10,7,4,13,22,12,14,16,6,6,16,14,12,22,12,21,
%U 6,9,12,1,12,9,6,21,12,23,31,15,17,19,7,7,19,17,15,31,23,11,20,5,8,11,14,1
%N Array T(n,k) (n>=1, k>=1) read by antidiagonals: T(n,n) = 1 for all n; fill in array above diagonal by symmetry; for row n, starting at diagonal T(n,n)=1, for k > n, T(n,k) = T(n,k-1)-(k-1) if this is positive and has not already appeared in this row, otherwise T(n,k) = T(n,k-1)+(k-1).
%H <a href="/index/Rea#Recaman">Index entries for sequences related to Recamán's sequence</a>
%e Array begins
%e 1 2 4 7 3 8 ...
%e 2 1 3 6 10 5 ...
%e 4 3 1 4 8 13 ...
%e 7 6 4 1 5 10 ...
%t T[n_, n_] = 1; T[n_, k_] /; k < n := T[n, k] = T[k, n]; T[n_, k_] := T[n, k] = If[t = T[n, k - 1] - (k - 1); t > 0 && FreeQ[Table[T[n, j], {j, 1, k - 1}], t], t, T[n, k - 1] + (k - 1)]; Table[T[n - k + 1, k], {n, 1, 13}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Feb 18 2018 *)
%Y Rows give A063733, A066203, A066204. Cf. A066201 for another version.
%K nonn,easy,tabl
%O 1,2
%A _N. J. A. Sloane_, Dec 16 2001
%E More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 06 2003