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A247749 Number T(n,k) of lattice paths from (0,0) to (n,0) that do not go below the x-axis or above the diagonal x=y, consist of steps u=(1,1), U=(1,3), H=(1,0), d=(1,-1) and D=(1,-3) for which the area below the path is k; triangle T(n,k), n>=0, read by rows. 3
1, 1, 1, 1, 1, 2, 1, 1, 3, 3, 2, 2, 0, 1, 1, 4, 6, 6, 6, 3, 4, 2, 1, 1, 1, 5, 10, 13, 15, 12, 14, 15, 9, 12, 5, 5, 1, 1, 1, 6, 15, 24, 32, 33, 37, 46, 40, 43, 34, 28, 23, 16, 10, 5, 2, 1, 1, 7, 21, 40, 61, 75, 88, 114, 122, 134, 137, 118, 127, 101, 99, 69, 68, 41, 38, 19, 17, 5, 5, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

LINKS

Alois P. Heinz, Rows n = 0..50, flattened

FORMULA

Sum_{k>=0}     T(n,k) = A240904(n).

Sum_{k>=1} k * T(n,k) = A247748(n).

EXAMPLE

Triangle T(n,k) begins:

1;

1;

1, 1;

1, 2,  1;

1, 3,  3,  2,  2,  0,  1;

1, 4,  6,  6,  6,  3,  4,  2,  1,  1;

1, 5, 10, 13, 15, 12, 14, 15,  9, 12,  5,  5,  1,  1;

1, 6, 15, 24, 32, 33, 37, 46, 40, 43, 34, 28, 23, 16, 10, 5, 2, 1;

MAPLE

b:= proc(x, y) option remember; `if`(y<0 or x<y, 0, `if`(x=0, 1,

      expand(add(z^(y+j/2)*b(x-1, y+j), j=[-1, -3, 0, 1, 3]))))

    end:

T:= n-> (p->seq(coeff(p, z, i), i=0..degree(p)))(b(n, 0)):

seq(T(n), n=0..10);

CROSSREFS

Cf. A240904, A247748.

Sequence in context: A131336 A052253 A271453 * A247367 A305321 A127838

Adjacent sequences:  A247746 A247747 A247748 * A247750 A247751 A247752

KEYWORD

nonn,tabf

AUTHOR

Alois P. Heinz, Sep 23 2014

STATUS

approved

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Last modified October 19 03:27 EDT 2018. Contains 316327 sequences. (Running on oeis4.)