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%I #9 Jul 14 2017 03:48:18
%S 1,2,6,26,168,1575,20355,347026,7544974,203740685,6689616195,
%T 262455558837,12125816088194,651621526430030,40298978168771397,
%U 2841833840854800621,226670892373665762106,20303920347033450136016,2029489177032856597849714
%N Cumulative boustrophedon transform of 1, 1, 1, 1, ...
%F See Maple code for precise description.
%p CBOUS2 := proc(a) option remember; local c,i,j,n,r: if whattype(a) <> list then RETURN([]); fi: n := min( nops(a), 60); for i from 0 to n-1 do c[i,0] := a[i+1]; od; 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); od; od; RETURN([seq(c[i,i],i=0..n-1)]); end:
%t nmax = 19; 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}]]]; Table[CBOUS2[Table[1, {n}]], {n, 0, nmax}] // Last (* _Jean-François Alcover_, Jul 14 2017, adapted from Maple *)
%Y See the triangles in A059433 and A059434.
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Jan 31 2001
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