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%I #28 Sep 13 2020 15:10:47
%S 1,2,3,3,1,2,4,2,3,5,5,6,1,4,7,6,4,5,7,8,9,7,5,6,1,4,10,8,8,9,4,2,3,5,
%T 6,10,9,7,8,3,1,2,10,5,4,10,8,9,6,2,3,7,11,12,13,11,12,7,10,5,1,9,8,6,
%U 14,15,12,10,11,13,6,4,14,7,9,8,16,17,13,11
%N Isosceles triangle read by rows in which each term is the least positive integer satisfying the condition that no row, diagonal, or antidiagonal contains a repeated term.
%C The n-th instance of 1 occurs at index A001844(n-1).
%C Records occur at 1, 2, 3, 7, 10, 12, 15, 20, 21, 27, 53, 54, 55, 65, ...
%F a(n) = A296339(n-1) + 1. - _Rémy Sigrist_, Sep 13 2020
%e Triangle begins:
%e 1
%e 2 3
%e 3 1 2
%e 4 2 3 5
%e 5 6 1 4 7
%e 6 4 X ...
%e The value for X is 5 because 1, 2, and 3 are on the diagonal; 4 and 6 are on the antidiagonal; and 4 and 6 are in the row. Therefore 5 is the smallest value that can be inserted so that no diagonal, antidiagonal, or row contains a repeated term.
%Y Analogs for other tilings: A269526 (square), A334049 (triangular).
%Y Cf. A001844, A274650, A274651, A288530, A288531, A296339.
%K tabl,nonn,more
%O 1,2
%A _Alec Jones_ and _Peter Kagey_, Sep 12 2020
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