A106327 -id:A106327 - cp's OEIS frontend

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

N. J. A. Sloane, May 29 2005

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

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

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

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 *)

More terms from Alois P. Heinz, Feb 08 2011

A106243 Triangle read by rows from left to right. However, triangle is constructed in the boustrophedon way, reading alternately right to left and left to right. Top entry is 1. In all later rows, initial entry is 0, other entries are sum of previous entry in that row plus sum of two entries above it in previous row.

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane, May 29 2005

			Triangle begins:
            1
          0   1
        1   1   0
      0   2   3   3
   13  13  11   6   0   (e.g., 11 = 6 + 3 + 2)
  0  26  50  67  73  73 (e.g., 50 = 26 + 13 + 11)

Cf. A007318, A008280, A008281, A106242. The row ends give A059294. Row sums give A106327.

T[0,0]:=1: for n from 0 to 12 do T[n,-1]:=0 od: for n from 0 to 12 do T[n,n+1]:=0 od: for n from 1 by 2 to 12 do T[n,0]:=0: for k from 1 to n do T[n,k]:=T[n,k-1]+T[n-1,k]+T[n-1,k-1] od: T[n+1,n+1]:=0: for j from 1 to n+1 do T[n+1,n+1-j]:=T[n+1,n+2-j]+T[n,n+1-j]+T[n,n-j] od: od: for n from 0 to 9 do seq(T[n,k],k=0..n) od; # yields sequence in triangular form; not necessarily the best Maple program # Emeric Deutsch, Aug 03 2005

More terms from Emeric Deutsch, Aug 03 2005

cp's OEIS Frontend

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

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