OFFSET
0,4
COMMENTS
Number of edges in the acyclic graph ("trellis") whose vertices are pairs (m,n) of natural numbers with 0 <= m <= i and 0 <= n <= j and which has edges from (m,n) to (m+1,n), (m,n+1) and (m+1,n+1). The number of edges of this graph is T(i,j), the array represented by the present sequence.
FORMULA
T(i, j) = 3*i*j + i + j.
Recurrence: T(i, 0) = i, T(0, j) = j, and T(i, j) = T(i-1, j) + T(i, j-1) - T(i-1, j-1) + 3 for i, j >= 1.
EXAMPLE
Square array T(i,j) (with rows i >= 0 and columns j >= 0) begins as follows:
0, 1, 2, 3, 4, ...
1, 5, 9, 13, 17, ...
2, 9, 16, 23, 30, ...
3, 13, 23, 33, 43, ...
4, 17, 30, 43, 56, ...
...
CROSSREFS
KEYWORD
AUTHOR
Martin Jansche (jansche(AT)acm.org), Jun 05 2003
STATUS
approved