A157518 Symmetric array T(n,m) of the number of 2-convex polygons with 2n horizontal and 2m vertical steps, read by antidiagonals.

6, 104, 104, 908, 1818, 908, 5298, 16560, 16560, 5298, 23261, 105510, 158768, 105510, 23261, 82603, 522325, 1086904, 1086904, 522325, 82603, 249245, 2125965, 5916957, 7962500, 5916957, 2125965, 249245, 661751, 7394811, 26917679

Offset

4,1

Comments

The first rows and columns, n<4 or m<4, are all zero and omitted from the sequence. The type of analysis of the paper puts this in the OEIS category "walk."

Links

Table of n, a(n) for n=4..34.

W. R. G. James, I. Jensen, and A. J. Guttmann, Exact generating function for 2-convex polygons, J. Phys A: Math. Theor. 41 (2008) 055001, eq (31).

Iwan Jensen, The anisotropic GF in Maple Friendly format.

Example

The array starts at n=m=4 as
......6.....104.....908....5298...23261...82603..249245..661751.1585672
....104....1818...16560..105510..522325.2125965.7394811.22623747
....908...16560..158768.1086904.5916957.26917679.105571678
...5298..105510.1086904.7962500.46811313.232629941
..23261..522325.5916957.46811313.296064058
..82603.2125965.26917679.232629941
.249245.7394811.105571678
.661751.22623747

Crossrefs

Sequence in context: A174481 A306205 A106303 * A001526 A295940 A106304

Adjacent sequences: A157515 A157516 A157517 * A157519 A157520 A157521

Keyword

nonn,tabl

Author

R. J. Mathar, Mar 02 2009

Status

approved