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A059433 Triangle formed when the cumulative boustrophedon transform is applied to 1, 1, 1, 1, ..., read by rows from left to right. 3

%I

%S 1,1,2,6,3,1,1,7,16,26,168,118,69,27,1,1,169,455,810,1192,1575,20355,

%T 16153,11952,7920,4343,1576,1,1,20356,56864,105324,161704,222427,

%U 284726,347026,7544974,6346546,5148119,3970048,2848841,1832958,978779,347027,1

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

%F From _Petros Hadjicostas_, Feb 16 2021: (Start)

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

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

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

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

%e Triangle T(i,j) (with rows i >= 0 and columns j = 0..i) begins:

%e 1;

%e 1, 2;

%e 6, 3, 1;

%e 1, 7, 16, 26;

%e 168, 118, 69, 27, 1;

%e 1, 169, 455, 810, 1192, 1575;

%e 20355, 16153, 11952, 7920, 4343, 1576, 1;

%e 1, 20356, 56864, 105324, 161704, 222427, 284726, 347026;

%e ... - _Petros Hadjicostas_, Feb 16 2021

%t 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-Fran├žois Alcover_, Jul 14 2017, adapted from Maple code for A059430 *)

%Y Cf. A059430, A059434.

%K nonn,tabl,easy

%O 0,3

%A _N. J. A. Sloane_, Jan 31 2001

%E More terms from _Floor van Lamoen_, Oct 08 2001

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Last modified September 17 05:34 EDT 2021. Contains 347478 sequences. (Running on oeis4.)