OFFSET
1,2
COMMENTS
The coefficients in the upper right triangle of the ED3 array (m>n) were found with the a(n,m) formula while the coefficients in the lower left triangle of the ED3 array (m<=n) were found with the recurrence relation, see below. We use for the array rows the letter n (>=1) and for the array columns the letter m (>=1).
LINKS
Johannes W. Meijer, The four Escher-Droste arrays, jpg image, Mar 08 2013.
FORMULA
a(n,m) = ((2*m-1)!!/ (2*m-2*n-1)!!)*int(sinh(y*(2*n-1))/(cosh(y))^(2*m),y=0..infinity) for m>n.
The (n-1)-differences of the n-th array row lead to the recurrence relation
sum((-1)^k*binomial(n-1,k)*a(n,m-k),k=0..n-1) = 2^(n-1)*(n-1)!*(2*n-1).
EXAMPLE
The ED3 array begins with:
1, 1, 1, 1, 1, 1, 1, 1, 1, 1
5, 11, 17, 23, 29, 35, 41, 47, 53, 59
23, 83, 183, 323, 503, 723, 983, 1283, 1623, 2003
167, 741, 2043, 4409, 8175, 13677, 21251, 31233, 43959, 59765
1473, 8169, 26529, 66345, 140865, 266793, 464289, 756969, 1171905, 1739625
16413, 106107, 398025, 1127655, 2678325, 5623443, 10768737, 19194495, 32297805, 51834795
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Johannes W. Meijer, Nov 10 2009
STATUS
approved