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Array read by antidiagonals: T(m,n) (m>=0, n>=0) = number of paths to origin (0,0) from grid point (m,n) in the Even Conant lattice.
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%I #13 Aug 23 2020 17:27:16

%S 1,1,1,1,2,1,1,3,1,1,1,1,4,2,1,1,1,5,2,1,1,1,2,6,2,1,2,1,1,3,0,8,3,3,

%T 1,1,1,1,3,0,11,0,4,2,1,1,1,1,3,11,0,4,2,1,1,1,2,1,4,14,11,4,6,1,2,1

%N Array read by antidiagonals: T(m,n) (m>=0, n>=0) = number of paths to origin (0,0) from grid point (m,n) in the Even Conant lattice.

%C The paths only use steps to the left and downwards.

%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).)

%H N. J. A. Sloane, <a href="/A337266/a337266.pdf">Portion of the Even Conant Lattice</a>, with number of paths to origin shown in red.

%F T(m,n) = v(m,n-1)*T(m,n-1)+h(m-1,n)*T(m-1,n), where v = A337263, h = A337264.

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

%e 1,

%e 1,1,

%e 1,2,1,

%e 1,3,1,1,

%e 1,1,4,2,1,

%e 1,1,5,2,1,1,

%e 1,2,6,2,1,2,1,

%e 1,3,0,8,3,3,1,1,

%e 1,1,3,0,11,0,4,2,1,

%e 1,1,1,3,11,0,4,2,1,1,

%e 1,2,1,4,14,11,4,6,1,2,1,

%e ...

%Y Cf. A328078, A328080, A337263, A337264, A337265.

%K nonn,tabl

%O 0,5

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