A287869 Wythoff array with one extra column, read by antidiagonals downwards.
1, 1, 3, 2, 4, 4, 3, 7, 6, 6, 5, 11, 10, 9, 8, 8, 18, 16, 15, 12, 9, 13, 29, 26, 24, 20, 14, 11, 21, 47, 42, 39, 32, 23, 17, 12, 34, 76, 68, 63, 52, 37, 28, 19, 14, 55, 123, 110, 102, 84, 60, 45, 31, 22, 16, 89, 199, 178, 165, 136, 97, 73, 50, 36, 25, 17
Offset: 1
Examples
The extended Wythoff array is the Wythoff array with two extra columns, giving the row number n and A000201(n), separated from the main array by a vertical bar: 0 1 | 1 2 3 5 8 13 21 34 55 89 144 ... 1 3 | 4 7 11 18 29 47 76 123 199 322 521 ... 2 4 | 6 10 16 26 42 68 110 178 288 466 754 ... 3 6 | 9 15 24 39 63 102 165 267 432 699 1131 ... 4 8 | 12 20 32 52 84 136 220 356 576 932 1508 ... 5 9 | 14 23 37 60 97 157 254 411 665 1076 1741 ... 6 11 | 17 28 45 73 118 191 309 500 809 1309 2118 ... 7 12 | 19 31 50 81 131 212 343 555 898 1453 2351 ... 8 14 | 22 36 58 94 152 246 398 644 1042 1686 2728 ... 9 16 | 25 41 66 107 173 280 453 733 1186 1919 3105 ... 10 17 | 27 44 71 115 186 301 487 788 1275 2063 3338 ... 11 19 | 30 49 79 ... 12 21 | 33 54 87 ... 13 22 | 35 57 92 ... 14 24 | 38 62 ... 15 25 | 40 65 ... 16 27 | 43 70 ... 17 29 | 46 75 ... 18 30 | 48 78 ... 19 32 | 51 83 ... 20 33 | 53 86 ... 21 35 | 56 91 ... 22 37 | 59 96 ... 23 38 | 61 99 ... 24 40 | 64 ... 25 42 | 67 ... 26 43 | 69 ... 27 45 | 72 ... 28 46 | 74 ... 29 48 | 77 ... 30 50 | 80 ... 31 51 | 82 ... 32 53 | 85 ... 33 55 | 88 ... 34 56 | 90 ... 35 58 | 93 ... 36 59 | 95 ... 37 61 | 98 ... 38 63 | ... ... The present sequence presents the array with just the rightmost extra column.
References
- Conway, John; Ryba, Alex; The extra Fibonacci series and the Empire State Building. Math. Intelligencer 38 (2016), no. 1, 41-48.