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Bidirectional 'Delannoy' variation of the Boustrophedon transform applied to all 1's sequence: Fill an triangular array in alternating directions. Let the first element of each row in that direction be equal to 1. Each next entry is given by T(n,k) = T(n,k +/- 1) + T(n-1,k-1) + T(n-1,k) + T(n-2,k-1), where the +/- depends on which is the previous element in the direction one is filling in the row. The final number of row n gives a(n).
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%I #6 Mar 02 2015 16:08:47

%S 1,2,6,22,105,631,4603,39469,388870,4327322,53670985,734069672,

%T 10975379510,178080287645,3116286236549,58502460526469

%N Bidirectional 'Delannoy' variation of the Boustrophedon transform applied to all 1's sequence: Fill an triangular array in alternating directions. Let the first element of each row in that direction be equal to 1. Each next entry is given by T(n,k) = T(n,k +/- 1) + T(n-1,k-1) + T(n-1,k) + T(n-2,k-1), where the +/- depends on which is the previous element in the direction one is filling in the row. The final number of row n gives a(n).

%H <a href="/index/Bo#boustrophedon">Index entries for sequences related to boustrophedon transform</a>

%Y Cf. A064641. Table: A064644, Delannoy numbers A008288.

%K nonn

%O 0,2

%A _Floor van Lamoen_, Oct 03 2001