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A059432 Triangle formed when cumulative boustrophedon transform is applied to 1, 0, 0, 0, ..., read by rows in natural order. 3
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified June 22 19:28 EDT 2021. Contains 345388 sequences. (Running on oeis4.)