A059432 Triangle formed when cumulative boustrophedon transform is applied to 1, 0, 0, 0, ..., read by rows in natural order.

1, 0, 1, 0, 1, 2, 0, 2, 5, 8, 0, 8, 21, 36, 51, 0, 51, 138, 246, 362, 478, 0, 478, 1318, 2404, 3628, 4903, 6178, 0, 6178, 17259, 31968, 49081, 67512, 86421, 105330, 0, 105330, 297081, 556344, 864688, 1205000, 1562571, 1926320, 2290069

Offset

0,6

Links

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

Formula

From Petros Hadjicostas, Feb 16 2021: (Start)

T(i,j) = T(i,j-1) + Sum_{r=1..j} T(i-1,i-r) for i >= 1 and 1 <= j <= i with T(i,0) = b(i+1) for i >= 0, where b(1) = 1 and b(i) = 0 for i >= 2. (The sequence b = (b(i): i >= 1) is the input sequence.)

T(i,j) = 2*T(i,j-1) - T(i,j-2) + T(i-1,i-j) for i >= 2 and 2 <= j <= i.

T(i,i) = A059429(i) = T(i+1,1) for i >= 0. (End)

Example

Triangle T(i,j) (with rows i >= 0 and columns j = 0..i) begins:
  1;
  0,    1;
  0,    1,     2;
  0,    2,     5,     8;
  0,    8,    21,    36,    51;
  0,   51,   138,   246,   362,   478;
  0,  478,  1318,  2404,  3628,  4903,  6178;
  0, 6178, 17259, 31968, 49081, 67512, 86421, 105330;
... - Petros Hadjicostas, Feb 16 2021

Maple

# This is a modification of N. J. A. Sloane's program from A059429:
CBOUS2 := proc(a) local c, i, j, n, r: option remember: if whattype(a) <> list then RETURN([]): end if: n := min(nops(a), 60): for i from 0 to n - 1 do c[i, 0] := a[i + 1]: end do: for i to n - 1 do for j to i do c[i, j] := c[i, j - 1] + add(c[i - 1, i - r], r = 1 .. j): end do: end do: RETURN([seq(seq(c[i, j], j = 0 .. i), i = 0 .. n - 1)]): end proc:
# To get the flattened triangle up to the 9th row, we type
CBOUS2([1, 0, 0, 0, 0, 0, 0, 0, 0, 0]); # Petros Hadjicostas, Feb 16 2021

Crossrefs

Cf. A059429, A059431.

Sequence in context: A011297 A110282 A024308 * A256488 A175631 A243816

Adjacent sequences: A059429 A059430 A059431 * A059433 A059434 A059435

Keyword

nonn,tabl,easy

Author

N. J. A. Sloane, Jan 31 2001

Status

approved