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Array read by antidiagonals: T(m,n) (m>=0, n>=0) = 3 if there is both an edge upward from grid point (m,n) in the Even Conant lattice and an edge to the right; = 2 if there is only an edge upward; = 1 if there is only an edge to the right; = 0 if neither of those edges are present.
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%I #19 Aug 23 2020 22:24:21

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

%T 3,3,3,1,1,0,2,0,2,2,3,3,3,1,3,3,0,3,2,3,3,3,2,3,2,2,1,2,2,3,2,3,3,1,

%U 3,1,3,0,2,2,3,1,3,3,3,1,2,1,1,1,3,3,3,1,2,2,3

%N Array read by antidiagonals: T(m,n) (m>=0, n>=0) = 3 if there is both an edge upward from grid point (m,n) in the Even Conant lattice and an edge to the right; = 2 if there is only an edge upward; = 1 if there is only an edge to the right; = 0 if neither of those edges are present.

%C In other words, T(m,n) = 2*v(m,n)+h(m,n), where v is given in A337263 and h is in A337264.

%C The '3' entries are in one-to-one correspondence with the cells in the Even Conant Lattice (see A328080).

%H N. J. A. Sloane, <a href="/A328078/a328078_2.txt">Notes on the Conant Gasket, the Conant Lattice, and Associated Sequences</a>, Preliminary version, Aug 23 2020

%H N. J. A. Sloane, <a href="/A328078/a328078_5.pdf">The Even Conant Lattice</a> (The grid points (m,n) are labeled with pairs v(m,n), h(m,n).)

%e The array begins as follows. The rows are shown in the appropriate order for looking at the first quadrant (that is, row 0 is at the bottom, then row 1, and so on):

%e r

%e row 7 = 3, 1, 1, 2, 3, 1, 2, 0, 3, 2, 0, 0, 3, 2, 3, 2, ...

%e row 6 = 3, 1, 1, 3, 2, 0, 3, 1, 2, 2, 0, 0, 3, 3, 2, 2, ...

%e row 5 = 3, 2, 0, 0, 3, 1, 2, 3, 2, 3, 1, 1, 2, 0, 3, 2, ...

%e row 4 = 3, 3, 1, 1, 2, 0, 2, 2, 3, 3, 1, 1, 2, 0, 2, 2, ...

%e row 3 = 3, 1, 2, 3, 2, 0, 3, 2, 3, 1, 2, 3, 2, 0, 3, 2, ...

%e row 2 = 3, 1, 2, 2, 3, 1, 2, 2, 3, 1, 2, 2, 3, 1, 2, 2, ...

%e row 1 = 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, ...

%e row 0 = 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, ...

%e The initial antidiagonals (starting in the bottom left corner) are:

%e [3]

%e [3, 3]

%e [3, 2, 3]

%e [3, 1, 3, 3]

%e [3, 1, 2, 2, 3]

%e [3, 3, 2, 2, 3, 3]

%e [3, 2, 1, 3, 3, 2, 3]

%e [3, 1, 0, 1, 2, 1, 3, 3]

%e [3, 1, 1, 0, 2, 0, 2, 2, 3]

%e [3, 3, 1, 3, 3, 0, 3, 2, 3, 3]

%e [3, 2, 3, 2, 2, 1, 2, 2, 3, 2, 3]

%e [3, 1, 3, 1, 3, 0, 2, 2, 3, 1, 3, 3]

%e [3, 1, 2, 1, 1, 1, 3, 3, 3, 1, 2, 2, 3]

%e ...

%p For Maple code see my "Notes".

%Y Cf. A328078, A328080, A337263, A337264.

%K nonn,tabl

%O 0,1

%A _N. J. A. Sloane_, Aug 22 2020