A059433 Triangle formed when the cumulative boustrophedon transform is applied to 1, 1, 1, 1, ..., read by rows from left to right.

1, 1, 2, 6, 3, 1, 1, 7, 16, 26, 168, 118, 69, 27, 1, 1, 169, 455, 810, 1192, 1575, 20355, 16153, 11952, 7920, 4343, 1576, 1, 1, 20356, 56864, 105324, 161704, 222427, 284726, 347026, 7544974, 6346546, 5148119, 3970048, 2848841, 1832958, 978779, 347027, 1

Offset

0,3

Links

Table of n, a(n) for n=0..44.

Formula

From Petros Hadjicostas, Feb 16 2021: (Start)

If 1 == i mod 2, then T(i,j) = A059434(i,j).

If 0 == i mod 2, then T(i,j) = A059434(i,i-j).

If 1 == i mod 2, then T(i,i) = A059434(i,i) = A059430(i).

If 0 == i mod 2, then T(i,0) = A059434(i,i) = A059430(i). (End)

Example

Triangle T(i,j) (with rows i >= 0 and columns j = 0..i) begins:
      1;
      1,     2;
      6,     3,     1;
      1,     7,    16,     26;
    168,   118,    69,     27,      1;
      1,   169,   455,    810,   1192,   1575;
  20355, 16153, 11952,   7920,   4343,   1576,      1;
      1, 20356, 56864, 105324, 161704, 222427, 284726, 347026;
  ... - Petros Hadjicostas, Feb 16 2021

Mathematica

nmax = 9; Clear[CBOUS2, c]; CBOUS2[a_List] := CBOUS2[a] = Module[{i, j, n, r }, n = Min[Length[a], nmax]; For[i = 0, i <= n - 1, i++, c[i, 0] = a[[i + 1]]]; For[i = n - 1, i <= nmax, i++, For[j = 1, j <= i, j++, c[i, j] = c[i, j - 1] + Sum[c[i - 1, i - r], {r, 1, j}]]]; Return[Table[ c[i, i], {i, 0, n - 1}]]]; Do[CBOUS2[Table[1, {n}]], {n, 0, nmax}]; Table[row = Table[c[i, j], {j, 0, i}]; If[OddQ[i], row, Reverse[row]], {i, 0, nmax - 1}] // Flatten (* Jean-François Alcover, Jul 14 2017, adapted from Maple code for A059430 *)

Crossrefs

Cf. A059430, A059434.

Sequence in context: A152549 A136759 A056129 * A021042 A136694 A164104

Adjacent sequences: A059430 A059431 A059432 * A059434 A059435 A059436

Keyword

nonn,tabl,easy

Author

N. J. A. Sloane, Jan 31 2001

Extensions

More terms from Floor van Lamoen, Oct 08 2001

Status

approved