A125226 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).

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, 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, 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

Offset: 1

Author

Gerald McGarvey, Jan 14 2007

Keywords

• nonn
• tabl

Comments

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).

Examples

			Array begins:
  1 1 0 0 0 0 0 ...
  1 1 2 1 0 0 0 ...
  0 2 4 4 3 1 0 ...
  ...
		

Crossrefs

Cf. A051292, A052945, A108014.

Programs

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],", ")))

Formula

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)