A296129 - OEIS

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

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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