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%I #5 Jun 29 2008 03:00:00
%S 1,1,1,2,1,1,3,1,1,1,5,2,1,1,1,8,2,1,1,1,1,13,4,2,1,1,1,1,21,4,2,1,1,
%T 1,1,1,34,8,2,2,1,1,1,1,1,55,8,5,2,1,1,1,1,1,1,89,16,5,2,2,1,1,1,1,1,
%U 1,144,16,5,2,2,1,1,1,1,1,1,1,233,32,11,6,2,2,1,1,1,1,1,1,1,377,32,11,6,2
%N Array read by antidiagonals: Minimizing absolutely ordered sequences of m-ary Huffman trees of maximum height; m > 1.
%H Alex Vinokur, <a href="http://arXiv.org/abs/cs/0411002">Fibonacci-Like Polynomials Produced by m-ary Huffman Codes for Absolutely Ordered Sequences</a>, E-print, 2004, 10 pages.
%F T[m, 0] = G[0, m-1], T[m, (i-1)*(m-1) + j] = G[i, m-1] where j = 1, 2, ..., (m-1); m > 1, i > 0. G[n, m] are Fibonacci-like polynomials defined by the recurrence relation G[0, m] = 1, G[1, m] = 1, G[2, m] = 2; G[n, m] = G[n-1, m] + m*G[n-2, m] when n > 2; m > 0.
%e Top left corner of array:
%e 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368 75025 121393
%e 1 1 1 2 2 4 4 8 8 16 16 32 32 64 64 128 128 256 256 512 512 1024 1024 2048 2048 4096
%e 1 1 1 1 2 2 2 5 5 5 11 11 11 26 26 26 59 59 59 137 137 137 314 314 314 725
%e 1 1 1 1 1 2 2 2 2 6 6 6 6 14 14 14 14 38 38 38 38 94 94 94 94 246
%e 1 1 1 1 1 1 2 2 2 2 2 7 7 7 7 7 17 17 17 17 17 52 52 52 52 52
%e 1 1 1 1 1 1 1 2 2 2 2 2 2 8 8 8 8 8 8 20 20 20 20 20 20 68
%e 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 9 9 9 9 9 9 9 23 23 23 23
%e 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 10 10 10 10 10 10 10 10 26
%e 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 11 11 11 11 11 11 11
%e 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 12 12 12 12 12
%e 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 13 13 13
%e 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 14
%e 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2
%e 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2
%e 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2
%K easy,nonn,tabl
%O 0,4
%A Alex Vinokur (alexvn(AT)barak-online.net), Nov 02 2004
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