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

%I A211312 #16 Feb 09 2019 07:25:24
%S A211312 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,
%T A211312 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,
%U A211312 1,2,0,2,2,0,2,1,0,1,1,2,2,1,1,1,1,1,1,1,2,2,1
%N A211312 Square array of Delannoy numbers D(i,j) mod 3 (i >= 0, j >= 0) read by antidiagonals.
%H A211312 Marko Razpet, <a href="http://dx.doi.org/10.1016/S0012-365X(01)00098-X">A self-similarity structure generated by king's walk</a>, Algebraic and topological methods in graph theory (Lake Bled, 1999). Discrete Math. 244 (2002), no. 1-3, 423--433. MR1844050 (2002k:05022)
%H A211312 Rémy Sigrist, <a href="/A211312/a211312.png">Colored representation of the first 1000 rows</a>
%F A211312 a(n) = sum(binomial(k, j) * binomial(n-j, k), j=0..n-k) mod 3. - _Johannes W. Meijer_, Jul 19 2013
%e A211312 Written as a triangle:
%e A211312 1,
%e A211312 1, 1,
%e A211312 1, 0, 1,
%e A211312 1, 2, 2, 1,
%e A211312 1, 1, 1, 1, 1,
%e A211312 1, 0, 1, 1, 0, 1,
%e A211312 1, 2, 2, 0, 2, 2, 1,
%e A211312 1, 1, 1, 0, 0, 1, 1, 1,
%e A211312 1, 0, 1, 0, 0, 0, 1, 0, 1,
%e A211312 ...
%p A211312 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
%t A211312 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_ *)
%Y A211312 Cf. A008288, A211312-A211315.
%K A211312 nonn,tabl
%O A211312 0,8
%A A211312 _N. J. A. Sloane_, Apr 15 2012