A205553 Square array by antidiagonals: C(max(i-1,2j-2),min(i-1,2j-2)), i>=1, j>=1.

1, 1, 1, 1, 2, 1, 1, 4, 1, 1, 1, 6, 6, 3, 1, 1, 8, 15, 4, 6, 1, 1, 10, 28, 20, 1, 10, 1, 1, 12, 45, 56, 15, 5, 15, 1, 1, 14, 66, 120, 70, 6, 15, 21, 1, 1, 16, 91, 220, 210, 56, 1, 35, 28, 1, 1, 18, 120, 364, 495, 252, 28, 7, 70, 36, 1, 1, 20, 153, 560, 1001, 792, 210, 8

Offset

1,5

Links

Table of n, a(n) for n=1..74.

Milan Janjic, Binomial Coefficients and Enumeration of Restricted Words, Journal of Integer Sequences, 2016, Vol 19, #16.7.3

Example

Northwest corner:
1....1....1....1....1
1....2....4....6....8
1....1....6....15...28
1....3....4....20...56
1....6....1....15...70

Mathematica

f[i_, j_] := Binomial[Max[i - 1, 2 j - 2], Min[i - 1, 2 j - 2]]
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: A340660 A136674 A144383 * A178411 A257598 A294580

Adjacent sequences: A205550 A205551 A205552 * A205554 A205555 A205556

Keyword

nonn,tabl

Author

Clark Kimberling, Jan 28 2012

Status

approved