A205548 Symmetric matrix by antidiagonals: C(max(i+1,j+1),min(i+1,j+1)), i>=1, j>=1.

1, 3, 3, 6, 1, 6, 10, 4, 4, 10, 15, 10, 1, 10, 15, 21, 20, 5, 5, 20, 21, 28, 35, 15, 1, 15, 35, 28, 36, 56, 35, 6, 6, 35, 56, 36, 45, 84, 70, 21, 1, 21, 70, 84, 45, 55, 120, 126, 56, 7, 7, 56, 126, 120, 55, 66, 165, 210, 126, 28, 1, 28, 126, 210, 165, 66, 78, 220

Offset

1,2

Links

Table of n, a(n) for n=1..68.

Example

Northwest corner:
1....3....6....10...15
3....1....4....10...20
6....4....1....5....15
10...10...5....1....6
15...20...15...6....1

Mathematica

g[k_] := k + 1;
f[i_, j_] := Binomial[Max[g[i], g[j]], Min[g[i], g[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}]]

Crossrefs

Cf. A205456.

Sequence in context: A189915 A085572 A342512 * A010609 A066519 A236258

Adjacent sequences: A205545 A205546 A205547 * A205549 A205550 A205551

Keyword

nonn,tabl

Author

Clark Kimberling, Jan 28 2012

Status

approved