A061926 - OEIS

%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