A211312 Square array of Delannoy numbers D(i,j) mod 3 (i >= 0, j >= 0) read by antidiagonals.

1, 1, 1, 1, 0, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 2, 2, 0, 2, 2, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 2, 2, 2, 0, 0, 2, 2, 2, 1, 1, 1, 1, 2, 2, 0, 2, 2, 1, 1, 1, 1, 0, 1, 2, 0, 2, 2, 0, 2, 1, 0, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1

Offset

0,8

Links

Table of n, a(n) for n=0..90.

Marko Razpet, A self-similarity structure generated by king's walk, Algebraic and topological methods in graph theory (Lake Bled, 1999). Discrete Math. 244 (2002), no. 1-3, 423--433. MR1844050 (2002k:05022)

Rémy Sigrist, Colored representation of the first 1000 rows

Formula

a(n) = sum(binomial(k, j) * binomial(n-j, k), j=0..n-k) mod 3. - Johannes W. Meijer, Jul 19 2013

Example

Written as a triangle:
1,
1, 1,
1, 0, 1,
1, 2, 2, 1,
1, 1, 1, 1, 1,
1, 0, 1, 1, 0, 1,
1, 2, 2, 0, 2, 2, 1,
1, 1, 1, 0, 0, 1, 1, 1,
1, 0, 1, 0, 0, 0, 1, 0, 1,
...

Maple

A211312 := proc(n, k): add(binomial(k, j) * binomial(n-j, k), j=0..n-k) mod 3 end: seq(seq(A211312(n, k), k=0..n), n=0..12); # Johannes W. Meijer, Jul 19 2013

Mathematica

a[n_, k_] := Mod[Binomial[n, k]*Hypergeometric2F1[-k, k-n, -n, -1], 3]; Table[a[n, k], {n, 0, 12}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jan 14 2014, after Johannes W. Meijer *)

Crossrefs

Cf. A008288, A211312-A211315.

Sequence in context: A131341 A124034 A332029 * A085978 A141044 A064284

Adjacent sequences: A211309 A211310 A211311 * A211313 A211314 A211315

Keyword

nonn,tabl

Author

N. J. A. Sloane, Apr 15 2012

Status

approved