A157518 - OEIS

%I #9 Feb 06 2024 16:23:01

%S 6,104,104,908,1818,908,5298,16560,16560,5298,23261,105510,158768,

%T 105510,23261,82603,522325,1086904,1086904,522325,82603,249245,

%U 2125965,5916957,7962500,5916957,2125965,249245,661751,7394811,26917679

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

%C 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."

%H W. R. G. James, I. Jensen, and A. J. Guttmann, <a href="http://dx.doi.org/10.1088/1751-8113/41/5/055001">Exact generating function for 2-convex polygons</a>, J. Phys A: Math. Theor. 41 (2008) 055001, eq (31).

%H Iwan Jensen, <a href="http://www.ms.unimelb.edu.au/~iwan/polygons/series/2-convex-anisotropic.txt">The anisotropic GF in Maple Friendly format</a>.

%e The array starts at n=m=4 as

%e ......6.....104.....908....5298...23261...82603..249245..661751.1585672

%e ....104....1818...16560..105510..522325.2125965.7394811.22623747

%e ....908...16560..158768.1086904.5916957.26917679.105571678

%e ...5298..105510.1086904.7962500.46811313.232629941

%e ..23261..522325.5916957.46811313.296064058

%e ..82603.2125965.26917679.232629941

%e .249245.7394811.105571678

%e .661751.22623747

%K nonn,tabl

%O 4,1

%A _R. J. Mathar_, Mar 02 2009