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URL: https://oeis.org/A383477

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A383477
Square array A(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where A(n,k) is the number of lattice paths from (0,0) to (n,k) using steps (1,0),(2,0),(3,0),(0,1).
2
1, 1, 1, 1, 2, 2, 1, 3, 5, 4, 1, 4, 9, 12, 7, 1, 5, 14, 25, 26, 13, 1, 6, 20, 44, 63, 56, 24, 1, 7, 27, 70, 125, 153, 118, 44, 1, 8, 35, 104, 220, 336, 359, 244, 81, 1, 9, 44, 147, 357, 646, 864, 819, 499, 149, 1, 10, 54, 200, 546, 1134, 1800, 2144, 1830, 1010, 274
OFFSET
0,5
FORMULA
A(n,k) = A(n-1,k) + A(n-2,k) + A(n-3,k) + A(n,k-1).
G.f.: 1 / (1 - x - x^2 - x^3 - y).
G.f. of column k: 1 / (1 - x - x^2 - x^3)^(k+1).
EXAMPLE
Square array A(n,k) begins:
1, 1, 1, 1, 1, 1, 1, ...
1, 2, 3, 4, 5, 6, 7, ...
2, 5, 9, 14, 20, 27, 35, ...
4, 12, 25, 44, 70, 104, 147, ...
7, 26, 63, 125, 220, 357, 546, ...
13, 56, 153, 336, 646, 1134, 1862, ...
24, 118, 359, 864, 1800, 3395, 5950, ...
PROG
(PARI) a(n, k) = my(x='x+O('x^(n+1)), y='y+O('y^(k+1))); polcoef(polcoef(1/(1-x-x^2-x^3-y), n), k);
CROSSREFS
Column k=0..2 give A000073(n+2), A073778(n+4), A292326(n-1).
Main diagonal gives A383478.
Sequence in context: A079956 A140717 A257005 * A160232 A026300 A099514
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Apr 28 2025
STATUS
approved