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

1,8

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).

Links

Table of n, a(n) for n=1..97.

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)

Example

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

Prog

(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], ", ")))

Crossrefs

Cf. A051292, A052945, A108014.

Sequence in context: A352361 A036865 A242249 * A281790 A245254 A059080

Adjacent sequences: A125223 A125224 A125225 * A125227 A125228 A125229

Keyword

nonn,tabl

Author

Gerald McGarvey, Jan 14 2007

Status

approved