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%I #7 Jan 24 2023 21:15:06
%S 1,0,1,0,1,1,0,1,1,1,0,0,2,1,1,0,0,1,2,1,1,0,0,2,2,2,1,1,0,0,1,3,2,2,
%T 1,1,0,0,1,3,4,2,2,1,1,0,0,0,3,4,4,2,2,1,1,0,0,0,3,5,5,4,2,2,1,1,0,0,
%U 0,3,5,6,5,4,2,2,1,1,0,0,0,2,7,7,7,5,4,2,2,1,1,0,0,0,2,6,9,8,7,5,4,2,2,1,1
%N Table by antidiagonals T(n,k) of number of partitions of k where the largest part is less than or equal to n and where there are no more than two of any particular sized part.
%F T(n, k) = T(n-1, k) + T(n-1, k-n) + T(n-1, k-2*n) with T(0, 0)=1 and T(n, k)=0 if n or k are negative. [Corrected by _Sean A. Irvine_, Jan 24 2023]
%e Table begins:
%e 1, 0, 0, 0, 0, 0, ...,
%e 1, 1, 1, 0, 0, 0, ...,
%e 1, 1, 2, 1, 2, 1, ...,
%e 1, 1, 2, 2, 3, 3, ...,
%e ...
%e T(3,5)=3 since 5 can be written as 3+2 or 3+1+1 or 2+2+1.
%Y Main diagonal is A000726.
%K nonn,tabl
%O 0,13
%A _Henry Bottomley_, Apr 20 2001
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