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A274534 Irregular triangle read by rows: T(n,k) = total number of k's in the first n antidiagonals of infinite Sudoku-type array A269526.

%I A274534 #18 Apr 15 2017 15:45:29
%S A274534 1,1,1,1,1,2,2,1,2,2,2,2,1,1,3,3,2,3,2,2,3,4,3,3,3,3,1,1,4,4,4,3,4,3,
%T A274534 2,2,1,1,5,4,4,4,5,4,3,3,2,1,1,5,5,4,5,6,5,4,4,3,1,1,1,1,5,5,5,6,7,6,
%U A274534 5,5,4,2,2,1,1,1,5,5,6,6,7,7,6,6,5,3,3,2,1,2,1,1,5,5,6,7,7,7,7,6,6,4,4,3,2,3,2,2,1,1
%N A274534 Irregular triangle read by rows: T(n,k) = total number of k's in the first n antidiagonals of infinite Sudoku-type array A269526.
%C A274534 T(n,k) is also the total number of (k-1)'s in the first n antidiagonals of the square array A274528.
%H A274534 Alois P. Heinz, <a href="/A274534/b274534.txt">Rows n = 1..175, flattened</a>
%e A274534 Triangle begins:
%e A274534 1;
%e A274534 1, 1, 1;
%e A274534 1, 2, 2, 1;
%e A274534 2, 2, 2, 2, 1, 1;
%e A274534 3, 3, 2, 3, 2, 2;
%e A274534 3, 4, 3, 3, 3, 3, 1, 1;
%e A274534 4, 4, 4, 3, 4, 3, 2, 2, 1, 1;
%e A274534 5, 4, 4, 4, 5, 4, 3, 3, 2, 1, 1;
%e A274534 5, 5, 4, 5, 6, 5, 4, 4, 3, 1, 1, 1, 1;
%e A274534 5, 5, 5, 6, 7, 6, 5, 5, 4, 2, 2, 1, 1, 1;
%e A274534 5, 5, 6, 6, 7, 7, 6, 6, 5, 3, 3, 2, 1, 2, 1, 1;
%e A274534 5, 5, 6, 7, 7, 7, 7, 6, 6, 4, 4, 3, 2, 3, 2, 2, 1, 1;
%e A274534 5, 5, 7, 8, 7, 8, 8, 7, 7, 5, 5, 4, 3, 4, 3, 3, 1, 1;
%e A274534 ...
%e A274534 For n = 3, the first three antidiagonals of the square array A269526 are [1], [3, 2], [2, 4, 3]. There are only one 1, two 2's, two 3's and only one 4, so the third row of the triangle is [1, 2, 2, 1].
%Y A274534 Cf. A269526, A274528.
%Y A274534 Row sums give A000217, n >= 1.
%Y A274534 Row lengths give A274529.
%K A274534 nonn,look,tabf
%O A274534 1,6
%A A274534 _Omar E. Pol_, Jun 30 2016