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A330601 Array T read by antidiagonals: T(m,n) is the number of lattice walks from (0,0) to (m,n) using one step from {(3,0), (2,1), (1,2), (0,3)} and all other steps from {(1,0), (0,1)}. 0
0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 4, 4, 4, 2, 3, 9, 12, 12, 9, 3, 4, 16, 28, 32, 28, 16, 4, 5, 25, 55, 75, 75, 55, 25, 5, 6, 36, 96, 156, 180, 156, 96, 36, 6, 7, 49, 154, 294, 392, 392, 294, 154, 49, 7, 8, 64, 232, 512, 784, 896, 784, 512, 232, 64, 8, 9, 81, 333, 837, 1458, 1890, 1890, 1458, 837, 333, 81, 9 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,11

LINKS

Table of n, a(n) for n=0..77.

FORMULA

T(m,n) = (m+n-2)*(binomial(m+n-2,m) + binomial(m+n-2,n)).

EXAMPLE

For (m,n) = (3,1), there are T(3,1) = 4 paths:

(3,0), (0,1)

(0,1), (3,0)

(2,1), (1,0)

(1,0), (2,1).

Array T(m,n) begins

n/m 0   1    2     3     4      5      6      7       8       9

0   0   0    0     1     2      3      4      5       6       7

1   0   0    1     4     9     16     25     36      49      64

2   0   1    4    12    28     55     96    154     232     333

3   1   4   12    32    75    156    294    512     837    1300

4   2   9   28    75   180    392    784   1458    2550    4235

5   3  16   55   156   392    896   1890   3720    6897   12144

6   4  25   96   294   784   1890   4200   8712   17028   31603

7   5  36  154   512  1458   3720   8712  19008   39039   76076

8   6  49  232   837  2550   6897  17028  39039   84084  171600

9   7  64  333  1300  4235  12144  31603  76076  171600  366080

PROG

(Sage)

def T(m, n):

    return (m+n-2)*(binomial(m+n-2, m) + binomial(m+n-2, n))

CROSSREFS

T(m,0) is A000027 for m >= 2.

T(m,1) is A000290 for m >= 1.

T(m,2) is A006000.

Sequence in context: A097541 A151819 A079560 * A088680 A143194 A036264

Adjacent sequences:  A330598 A330599 A330600 * A330602 A330603 A330604

KEYWORD

tabl,nonn

AUTHOR

Steven Klee, Dec 19 2019

STATUS

approved

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Last modified August 8 21:55 EDT 2022. Contains 356016 sequences. (Running on oeis4.)