A059674 -id:A059674 - cp's OEIS frontend

A205456 Symmetric matrix by antidiagonals: C(max(i,j),min(i,j)), i>=1, j>=1.

1, 2, 2, 3, 1, 3, 4, 3, 3, 4, 5, 6, 1, 6, 5, 6, 10, 4, 4, 10, 6, 7, 15, 10, 1, 10, 15, 7, 8, 21, 20, 5, 5, 20, 21, 8, 9, 28, 35, 15, 1, 15, 35, 28, 9, 10, 36, 56, 35, 6, 6, 35, 56, 36, 10, 11, 45, 84, 70, 21, 1, 21, 70, 84, 45, 11, 12, 55, 120, 126, 56, 7, 7, 56, 126, 120

Offset: 1

Clark Kimberling, Jan 28 2012

C(max(i,j),min(i,j))=number of {E,N,NE} paths from (0,0) to (i,j). Each step of a path is represented by (a,b)->(a+1,b) or (a,b)->(a,b+1) or (a,b)->(a+1,b+1). To include paths from (0,0) to points (a,0) and (0,b), see A059674.

			Northwest corner:
1....2....3....4....5....6....7
2....1....3....6....10...15...21
3....3....1....4....10...20...35
4....6....4....1....5....15...35
5....10...10...5....1....6....21

Cf. A205457, A205548, A059674.

f[i_, j_] := Binomial[Max[i, j], Min[i, j]]
TableForm[Table[f[i, j], {i, 1, 10}, {j, 1, 10}]]
Flatten[Table[f[i, n + 1 - i], {n, 1, 14}, {i, 1, n}]]

cp's OEIS Frontend

A205456 Symmetric matrix by antidiagonals: C(max(i,j),min(i,j)), i>=1, j>=1.

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