A296129 Array read by antidiagonals: the number of directed elements with area n on the lattice T_{2k+1}.

0, 1, 0, 2, 1, 0, 4, 4, 1, 0, 8, 19, 6, 1, 0, 16, 96, 46, 8, 1, 0, 32, 501, 376, 85, 10, 1, 0, 64, 2668, 3176, 960, 136, 12, 1, 0, 128, 14407, 27384, 11201, 1960, 199, 14, 1, 0, 256, 78592, 239464, 133400, 29176, 3488, 274, 16, 1, 0, 512, 432073, 2115712, 1611317, 443296, 63141, 5656, 361, 18, 1, 0, 1024, 2390004

Offset

0,4

Links

Table of n, a(n) for n=0..67.

S. Corteel, A. Denise, D. Gouyou-Beauchamps, Bijections for directed animals on infinite families of lattices, Ann. Combinat. 4 (3-4) (2000), 269-284, Eq. (5.14).

Example

The array starts with rows n>=0 and columns k>=0 as:
0,      0,      0,      0,      0,      0,      0,      0,      0, ...
1,      1,      1,      1,      1,      1,      1,      1,      1, ...
2,      4,      6,      8,     10,     12,     14,     16,     18, ...
4,     19,     46,     85,    136,    199,    274,    361,    460, ...
8,     96,    376,    960,   1960,   3488,   5656,   8576,  12360, ...
16,    501,   3176,  11201,  29176,  63141, 120576, 210401, 342976, ...
32,   2668,  27384, 133400, 443296,1166628,2623544,5268400,9713376, ...

Maple

A296129 := proc(n, k)
    local a, i, l;
    a := 0 ;
    for i from 1 to n do
        add( binomial(i, l)*binomial((k+1)*l, i-1), l=0..i) ;
        a := a+ %*binomial(n-1, i-1)*(i*k+1)/(2*i*(k+1)) ;
    end do;
    a ;
end proc:

Crossrefs

Cf. A047781 (column k=1).

Sequence in context: A051623 A244124 A183190 * A276544 A214753 A158454

Adjacent sequences: A296126 A296127 A296128 * A296130 A296131 A296132

Keyword

nonn,tabl,easy

Author

R. J. Mathar, Dec 05 2017

Status

approved