%I #4 Jun 29 2008 03:00:00

%S 1,1,1,2,1,1,3,2,1,1,5,4,2,1,1,8,8,5,2,1,1,13,16,11,6,2,1,1,21,32,26,

%T 14,7,2,1,1,34,64,59,38,17,8,2,1,1,55,128,137,94,52,20,9,2,1,1,89,256,

%U 314,246,137,68,23,10,2,1,1,144,512,725,622,397,188,86,26,11,2,1,1,233,1024

%N Array read by antidiagonals: Numerical sequences of Fibonacci-like polynomials produced by m-ary Huffman trees of maximum height for absolutely ordered sequences.

%H Alex Vinokur, <a href="http://arXiv.org/abs/cs/0410013">Fibonacci connection between Huffman codes and Wythoff array</a>, E-print, 2004, 10 pages.

%F T[0, m] = 1, T[1, m] = 1, T[2, m] = 2; T[n, m] = T[n-1, m] + m*T[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

%e 1 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192 16384 32768 65536 131072 262144 524288

%e 1 1 2 5 11 26 59 137 314 725 1667 3842 8843 20369 46898 108005 248699 572714 1318811 3036953 6993386

%e 1 1 2 6 14 38 94 246 622 1606 4094 10518 26894 68966 176542 452406 1158574 2968198 7602494 19475286 49885262

%e 1 1 2 7 17 52 137 397 1082 3067 8477 23812 66197 185257 516242 1442527 4023737 11236372 31355057 87536917 244312202

%e 1 1 2 8 20 68 188 596 1724 5300 15644 47444 141308 425972 1273820 3829652 11472572 34450484 103285916 309988820 929704316

%e 1 1 2 9 23 86 247 849 2578 8521 26567 86214 272183 875681 2780962 8910729 28377463 90752566 289394807 924662769 2950426418

%e 1 1 2 10 26 106 314 1162 3674 12970 42362 146122 485018 1653994 5534138 18766090 63039194 213167914 717481466 2422824778 8162676506

%e 1 1 2 11 29 128 389 1541 5042 18911 64289 234488 813089 2923481 10241282 36552611 128724149 457697648 1616214989 5735493821 20281428722

%e 1 1 2 12 32 152 472 1992 6712 26632 93752 360072 1297592 4898312 17874232 66857352 245599672 914173192 3370169912 12511901832 46213600952

%e 1 1 2 13 35 178 563 2521 8714 36445 132299 533194 1988483 7853617 29726930 116116717 443112947 1720396834 6594639251 25519004425 98060036186

%e 1 1 2 14 38 206 662 3134 11078 48686 181622 765854 2945318 12135566 47479382 193106174 762858758 3080132846 12234437942 49196032094 196009287398

%e 1 1 2 15 41 236 769 3837 13834 63715 243557 1071852 4238093 18172169 73267378 309505575 1261981489 5285553964 21691313321 90403514853 372390588026

%e 1 1 2 16 44 268 884 4636 17012 81916 320084 1466908 5948084 26484796 109757972 480545116 2017156724 8744788348 36984982484 159412019356 677201774132

%e 1 1 2 17 47 302 1007 5537 20642 103697 413327 1968782 8168687 37700417 160230722 725736977 3129197807 14015252462 60953219567 271182006497 1185480300002

%e 1 1 2 18 50 338 1138 6546 24754 129490 525554 2597394 11006258 52564562 228664690 1069697682 4728332722 21843495634 97496819186 446992749330 2006941856306

%e 1 1 2 19 53 376 1277 7669 29378 159751 659177 3374944 14580953 71955001 319831202 1543066219 6980196653 33212322376 151875665477 716485145869 3298371458978

%e 1 1 2 20 56 416 1424 8912 34544 194960 816752 4326032 19027568 96896144 439392368 2183522960 10092585584 49395998864 231062539376 1120190518928 5279316227696

%e 1 1 2 21 59 458 1579 10281 40282 235621 1000979 5477778 24496379 128574161 594005362 3036914421 14323016299 72024390298 344161699979 1712625115641 8251697415242

%e 1 1 2 22 62 502 1742 11782 46622 282262 1214702 6859942 31153982 168352822 791432462 4158488902 19987138142 103156916182 502899679022 2566038002662 12624031583102

%e 1 1 2 23 65 548 1913 13421 53594 335435 1460909 8505044 39184133 217790057 1040656850 5614248047 27468041897 145367250884 722196130721 3774908399285 18941027144426

%K easy,nonn,tabl

%O 0,4

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