A098824 Array read by antidiagonals: Minimizing absolutely ordered sequences of m-ary Huffman trees of maximum height; m > 1.

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, 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, 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

Offset

0,4

Links

Table of n, a(n) for n=0..95.

Alex Vinokur, Fibonacci-Like Polynomials Produced by m-ary Huffman Codes for Absolutely Ordered Sequences, E-print, 2004, 10 pages.

Formula

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.

Example

Top left corner of array:
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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

Crossrefs

Sequence in context: A182285 A160182 A195825 * A181651 A124032 A254046

Adjacent sequences: A098821 A098822 A098823 * A098825 A098826 A098827

Keyword

easy,nonn,tabl

Author

Alex Vinokur (alexvn(AT)barak-online.net), Nov 02 2004

Status

approved