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%I #10 Nov 19 2017 01:41:32
%S 1,1,1,2,2,2,6,4,4,6,20,10,8,10,20,68,30,18,18,30,68,232,98,48,36,48,
%T 98,232,792,330,146,84,84,146,330,792,2704,1122,476,230,168,230,476,
%U 1122,2704,9232,3826,1598,706,398,398,706,1598,3826,9232,31520,13058,5424
%N Symmetric square table, read by antidiagonals, such that antidiagonal sums form the first row shifted left: T(0,0)=1, T(0,k) = Sum_{m=0..k-1} T(m,k-1-m) when k > 0; and T(n,k) = T(n-1,k) + T(n,k-1) when n > 0, k > 0.
%C Antidiagonal sums give A006012. Table is symmetric under transpose, so that first column equals the first row. Second row gives partial sums of first row.
%F T(0,0)=1, T(0,1)=1, T(0,n) = 4*T(0,n-1) - 2*T(0,n-2) when n >= 2.
%e Table begins:
%e 1, 1, 2, 6, 20, 68, 232, 792, ...
%e 1, 2, 4, 10, 30, 98, 330, 1122, ...
%e 2, 4, 8, 18, 48, 146, 476, 1598, ...
%e 6, 10, 18, 36, 84, 230, 706, 2304, ...
%e 20, 30, 48, 84, 168, 398, 1104, 3408, ...
%e 68, 98, 146, 230, 398, 796, 1900, 5308, ...
%e 232, 330, 476, 706, 1104, 1900, 3800, 9108, ...
%e 792, 1122, 1598, 2304, 3408, 5308, 9108, 18216, ...
%e 2704, 3826, 5424, 7728, 11136, 16444, 25552, 43768, ...
%e 9232, 13058, 18482, 26210, 37346, 53790, 79342, 123110, ...
%Y Cf. A006012 (row sums), A084868 (main diagonal).
%K nonn,tabl
%O 0,4
%A _Paul D. Hanna_, Jun 10 2003, Jun 11 2003
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