A098950 Array read by antidiagonals: minimizing k-ordered sequences of maximum height Huffman tree.

1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 4, 2, 1, 1, 1, 7, 4, 2, 1, 1, 1, 11, 6, 3, 2, 1, 1, 1, 18, 10, 6, 3, 2, 1, 1, 1, 29, 16, 9, 5, 3, 2, 1, 1, 1, 47, 26, 15, 9, 5, 3, 2, 1, 1, 1, 76, 42, 24, 14, 8, 5, 3, 2, 1, 1, 1, 123, 68, 39, 23, 14, 8, 5, 3, 2, 1, 1, 1, 199, 110, 63, 37, 22, 13, 8, 5, 3, 2, 1, 1, 1, 322

Offset

0,7

Links

Table of n, a(n) for n=0..91.

Alex Vinokur, Fibonacci connection between Huffman codes and Wythoff array, E-print

Alex Vinokur, Fibonacci connection between Huffman codes and Wythoff array, Posting to news:sci.math

Formula

T[k, 1] = 1; T[k, i] = Fib(i-1) when 2<=i<=(k+3); T[k, i] = w[Fib(k+2), i-(k+3)] when i>=(k+3); w[i, j] is (i, j)-th element of the generalized Wythoff array

Example

Top left corner of array:
1 1 1 3 4 7 11 18 29 47 76 123 199 322 521 843 1364 2207 3571 5778 9349...
1 1 1 2 4 6 10 16 26 42 68 110 178 288 466 754 1220 1974 3194 5168 8362...
1 1 1 2 3 6 9 15 24 39 63 102 165 267 432 699 1131 1830 2961 4791 7752...
1 1 1 2 3 5 9 14 23 37 60 97 157 254 411 665 1076 1741 2817 4558 7375...
1 1 1 2 3 5 8 14 22 36 58 94 152 246 398 644 1042 1686 2728 4414 7142...
1 1 1 2 3 5 8 13 22 35 57 92 149 241 390 631 1021 1652 2673 4325 6998...
1 1 1 2 3 5 8 13 21 35 56 91 147 238 385 623 1008 1631 2639 4270 6909...
1 1 1 2 3 5 8 13 21 34 56 90 146 236 382 618 1000 1618 2618 4236 6854...
1 1 1 2 3 5 8 13 21 34 55 90 145 235 380 615 995 1610 2605 4215 6820...
1 1 1 2 3 5 8 13 21 34 55 89 145 234 379 613 992 1605 2597 4202 6799...
1 1 1 2 3 5 8 13 21 34 55 89 144 234 378 612 990 1602 2592 4194 6786...
1 1 1 2 3 5 8 13 21 34 55 89 144 233 378 611 989 1600 2589 4189 6778...
1 1 1 2 3 5 8 13 21 34 55 89 144 233 377 611 988 1599 2587 4186 6773...
1 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 988 1598 2586 4184 6770...
1 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1598 2585 4183 6768...
1 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2585 4182 6767...
1 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4182 6766...
1 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6766...
1 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765...
1 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765...
1 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765...

Crossrefs

Cf. A000045, A035513.

Sequence in context: A364096 A348028 A059619 * A318873 A346403 A295924

Adjacent sequences: A098947 A098948 A098949 * A098951 A098952 A098953

Keyword

easy,nonn,tabl

Author

Alex Vinokur (alexvn(AT)barak-online.net), Oct 21 2004

Status

approved