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Number of neighbors of each new term in a right triangle read by rows.
8

%I #30 Nov 23 2016 11:29:44

%S 0,1,2,2,3,2,2,4,3,2,2,4,4,3,2,2,4,4,4,3,2,2,4,4,4,4,3,2,2,4,4,4,4,4,

%T 3,2,2,4,4,4,4,4,4,3,2,2,4,4,4,4,4,4,4,3,2,2,4,4,4,4,4,4,4,4,3,2,2,4,

%U 4,4,4,4,4,4,4,4,3,2,2,4,4,4,4,4,4,4,4,4,4,3,2,2,4,4,4,4,4,4,4,4,4,4,4,3,2

%N Number of neighbors of each new term in a right triangle read by rows.

%C To evaluate T(n,k) consider only the neighbors of T(n,k) that are present in the triangle when T(n,k) should be a new term in the triangle.

%C Apart from the first column and the first two diagonals the rest of the elements are 4's.

%C For the same idea but for an isosceles triangle see A275015; for a square array see A278290, for a square spiral see A278354; and for a hexagonal spiral see A047931.

%e Triangle begins:

%e 0;

%e 1, 2;

%e 2, 3, 2;

%e 2, 4, 3, 2;

%e 2, 4, 4, 3, 2;

%e 2, 4, 4, 4, 3, 2;

%e 2, 4, 4, 4, 4, 3, 2;

%e 2, 4, 4, 4, 4, 4, 3, 2;

%e 2, 4, 4, 4, 4, 4, 4, 3, 2;

%e 2, 4, 4, 4, 4, 4, 4, 4, 3, 2;

%e ...

%Y Apart from the initial zero, row sums give A004767.

%Y Column 1 is A130130.

%Y Columns > 1 give the terms greater than 1 of A158411.

%Y Right border gives 0 together with A007395, also twice A057427.

%Y Second right border gives A122553.

%Y Cf. A047931, A274912, A274913, A275015, A278290, A278317, A278354,

%K nonn,tabl

%O 1,3

%A _Omar E. Pol_, Nov 18 2016