A106242 Same triangle as A106243, but with rows read in boustrophedon manner, i.e., in the order in which they were created.

1, 0, 1, 0, 1, 1, 0, 2, 3, 3, 0, 6, 11, 13, 13, 0, 26, 50, 67, 73, 73, 0, 146, 286, 403, 479, 505, 505, 0, 1010, 1994, 2876, 3565, 3997, 4143, 4143, 0, 8286, 16426, 23988, 30429, 35299, 38303, 39313, 39313, 0, 78626, 156242, 229844, 295572, 349989, 390403, 415115, 423401, 423401

Offset: 0

Author

N. J. A. Sloane, May 29 2005

Keywords

• nonn
• tabl
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10010

Crossrefs

Right-hand diagonal is A059294. Cf. A106243. Row sums give A106327.

Programs

Maple

T:= proc(n, k) option remember;
      local t;
      if n<1 or k<1 then 0
    elif n=1 and k=1 then 1
    elif n=1 and irem(k, 2)=1 or k=1 and irem(n, 2)=0 then 0
    else t:= 1-2*irem(n+k, 2);
             T(n-t, k+t) + T(n, k-1)+T(n-1, k)
      fi
    end:
seq (`if` (irem(d, 2)=1,
  seq (T(d-k, k), k=1..d-1),
  seq (T(n, d-n), n=1..d-1)), d=2..11);  # Alois P. Heinz, Feb 08 2011

Mathematica

T[n_, k_] := T[n, k] = Module[{t}, Which[n<1 || k<1, 0, n == 1 && k == 1, 1, n == 1 && Mod[k, 2] == 1 || k == 1 && Mod[n, 2] == 0, 0, True, t = 1 - 2*Mod[n+k, 2]; T[n-t, k+t] + T[n, k-1] + T[n-1, k]]]; Table[If[Mod[d, 2] == 1, Table[T[d-k, k], {k, 1, d-1}], Table[T[n, d-n], {n, 1, d-1}]], {d, 2, 11}] // Flatten (* Jean-François Alcover, Jan 14 2014, translated from Alois P. Heinz's Maple code *)

Extensions

More terms from Alois P. Heinz, Feb 08 2011