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%I #6 Jun 28 2017 23:34:05
%S 1,1,1,0,1,0,0,2,2,0,0,1,4,1,0,0,0,4,4,0,0,0,0,3,9,3,0,0,0,0,1,11,11,
%T 1,0,0,0,0,0,8,21,8,0,0,0,0,0,0,4,27,27,4,0,0,0,0,0,0,1,23,52,23,1,0,
%U 0,0,0,0,0,0,13,67,67,13,0,0,0,0,0,0,0,0,5,62,127,62,5,0,0,0,0,0,0,0,0,1,41
%N Array, read by antidiagonals, where A(1,1) = A(1,2) = A(2,1) = A(2,2) = 1, A(n,k) = 0 if n<1 or k<1, otherwise A(n,k) = A(n-2,k-2) + A(n-1,k-2) + A(n-2,k-1) + A(n-1,k-1).
%C It appears that the main diagonal (1,1,4,9,21,...) is A051292 (Whitney number of level n of the lattice of the ideals of the crown of size 2 n). It appears that if b(n) = the n-th antidiagonal sum - A108014(n-1) then the sequence b(n) is the sequence 1,0,-2,0,1,0 repeated. n-th row sum = A052945(n).
%F A(1,1) = A(1,2) = A(2,1) = A(2,2) = 1, A(n,k) = 0 if n<1 or k<1, otherwise A(n,k) = A(n-2,k-2) + A(n-1,k-2) + A(n-2,k-1) + A(n-1,k-1)
%e Example:
%e Array begins
%e 1 1 0 0 0 0 0 ...
%e 1 1 2 1 0 0 0 ...
%e 0 2 4 4 3 1 0 ...
%e ...
%o (PARI) A=matrix(22,22);A[1,1]=1;A[1,2]=1;A[2,1]=1;A[2,2]=1;A[3,2]=2;A[2,3]=2;A[2,4]=1;A[4,2]=1; for(n=3,22,for(k=3,22,A[n,k]=A[n-2,k-2]+A[n-1,k-2]+A[n-2,k-1]+A[n-1,k-1])); for(n=1,22,for(i=1,n,print1(A[n-i+1,i],", ")))
%Y Cf. A051292, A052945, A108014.
%K nonn,tabl
%O 1,8
%A _Gerald McGarvey_, Jan 14 2007
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