OFFSET
1,2
COMMENTS
The array is always extended by its antidiagonals with the smallest term not yet present that doesn't lead to a contradiction. The sequence is thus the lexicographically earliest of its kind.
This regular pattern appears: . . . . 3 . . 4 5 . . 6 7 8 . . 9 10 11 12 . . 13 14 15 16 17 . . 18 19 20 21 22 23 . . This is the first time that these terms appear in the sequence. So it is possible to calculate the terms of this pattern. - Bernard Schott, Jun 03 2019
FORMULA
a(n*(n+1)/2) = a(n*(n-1)/2+1) = a(n). - Rémy Sigrist, May 21 2019
T(n+1,k+1) = A000027(n,k) + 2 if both sequences are read as square arrays. - Charlie Neder, Jun 03 2019
From Bernard Schott, Jun 03 2019: (Start)
For 2 <= q <= k:
a(k*(k+1)/2 + 2) = (k-2)*(k-1)/2 + 3.
a(k*(k+1)/2 + q) = (k-2)*(k-1)/2 + q + 1.
a(k*(k+1)/2 + k) = a(k*(k+3)/2) = (k-2)*(k-1)/2 + k + 1 = (k^2-k+4)/2. (End)
EXAMPLE
Array:
1 2 2 2 3 2 2 4 5 2 3 ...
2 3 4 6 9 13 18 24 31 39 48 ...
2 5 7 10 14 19 25 32 40 49 59 ...
2 8 11 15 20 26 33 41 50 60 71 ...
3 12 16 21 27 34 42 51 61 72 84 ...
2 17 22 28 35 43 52 62 73 85 98 ...
2 23 29 36 44 53 63 74 86 99 113 ...
4 30 37 45 54 61 75 87 100 112 129 ...
5 38 46 55 62 76 88 101 113 130 146 ...
2 47 56 63 77 89 102 114 131 147 164 ...
3 57 64 78 90 101 115 132 148 165 183 ...
...
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Eric Angelini, May 21 2019
STATUS
approved