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%I #7 Mar 14 2023 18:30:06
%S 0,1,0,0,1,0,1,1,1,0,0,2,2,1,0,1,2,3,3,1,0,0,3,4,6,4,1,0,1,3,5,10,9,5,
%T 1,0,0,4,6,15,16,14,6,1,0,1,4,7,21,25,30,19,7,1,0,0,5,8,28,36,55,44,
%U 26,8,1,0,1,5,9,36,49,91,85,70,33,9,1,0,0,6,10,45,64,140,146,155,96,42,10
%N Square table by antidiagonals where odd rows are partial sums of previous row, even rows are sums of pairs of values in previous row and initial row is 0 and 1 alternating.
%F T(0, 2*k) = 0, T(0, 2*k+1) = 1, T(n, 0) = 0, T(2*n, k) = T(2*n-1, k-1) + T(2*n-1, k), T(2*n+1, k) = T(2*n+1, k-1) + T(2*n, k). - _Sean A. Irvine_, Mar 14 2023
%e From _Sean A. Irvine_, Mar 14 2023: (Start)
%e Table begins:
%e 0 1 0 1 0 1 0 1
%e 0 1 1 2 2 3 3 4
%e 0 1 2 3 4 5 6 7
%e 0 1 3 6 10 15 21 28
%e 0 1 4 9 16 25 36 49
%e 0 1 5 14 30 55 91 140
%e 0 1 6 19 44 85 146 231
%e 0 1 7 26 70 155 301 532
%e (End)
%Y Rows are A000035, A004526, A001477, A000217, A000290, A000330, A005900, A006325, A014820, A061927. Columns are A000004, A000012, A001477, A061925.
%K nonn,tabl
%O 0,12
%A _Henry Bottomley_, May 17 2001