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%I #7 Aug 20 2015 05:29:08
%S 0,1,1,2,2,2,2,3,3,2,3,3,4,3,3,3,4,4,4,4,3,3,4,5,4,5,4,3,3,4,5,5,5,5,
%T 4,3,4,4,5,5,6,5,5,4,4,4,5,5,5,6,6,5,5,5,4,4,5,6,5,6,6,6,5,6,5,4,4,5,
%U 6,6,6,6,6,6,6,6,5,4,4,5,6,6,7,6,6,6,7,6,6,5,4,4,5,6,6,7,7,6,6,7,7,6,6,5,4
%N Triangle read by rows: T(m,n)=A029837(m)+A029837(n), where (m,n)=(1,1); (2,1), (1,2); (3,1), (2,2), (1,3); ...
%C A029837(n) is the smallest k such that 2^k>=n. T(m,n) is the solution to the following simple problem. What is the minimum number of cuts needed to divide a sheet of paper whose sides are in the ratio m:n into mn square pieces of equal size? (A single cut means either cutting one rectangle into two smaller rectangles or placing two or more sheets on top of one another and cutting through the lot in one go.)
%e Array begins
%e 0
%e 1 1
%e 2 2 2
%e 2 3 3 2
%e 3 3 4 3 3
%t t[n_, k_] := Ceiling[Log[2, k]] + Ceiling[Log[2, n-k+1]]; Table[t[n, k], {n, 1, 14}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Feb 24 2015 *)
%Y Cf. A029837.
%K easy,nonn,tabl
%O 1,4
%A _Paul Boddington_, Jul 26 2004
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