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A375001
Square array read by antidiagonals: T(n,k) is the position of the last requested element when the elements of the k-th composition (in standard order) are requested from a self-organizing list initialized to (1, 2, 3, ...), using the move-ahead(n) updating strategy; n >= 0, k >= 1.
3
1, 2, 1, 1, 2, 1, 3, 1, 2, 1, 1, 3, 1, 2, 1, 2, 2, 3, 1, 2, 1, 1, 2, 2, 3, 1, 2, 1, 4, 1, 2, 2, 3, 1, 2, 1, 1, 4, 1, 2, 2, 3, 1, 2, 1, 2, 1, 4, 1, 2, 2, 3, 1, 2, 1, 1, 1, 2, 4, 1, 2, 2, 3, 1, 2, 1, 3, 1, 1, 2, 4, 1, 2, 2, 3, 1, 2, 1, 1, 3, 1, 1, 2, 4, 1, 2, 2, 3, 1, 2, 1
OFFSET
0,2
COMMENTS
See A374996 for details.
FORMULA
T(0,k) = A007814(k) + 1.
T(1,k) = A374998(k).
T(n,k) = A374997(k) if n >= A333766(k)-1.
T(n,k) = A374996(n,k) - A374996(n,A025480(k-1)).
Sum_{j=1..m} T(n,k*2^j+2^(j-1)) = m*(m+1)/2 if m >= A333766(k). This is a consequence of the fact that the first m positions of the list are occupied by the elements 1, ..., m, as long as no element larger than m has been requested so far.
EXAMPLE
Array begins:
n\k| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
---+--------------------------------------------
0 | 1 2 1 3 1 2 1 4 1 2 1 3 1 2 1
1 | 1 2 1 3 2 2 1 4 1 1 1 3 2 2 1
2 | 1 2 1 3 2 2 1 4 2 1 1 3 2 2 1
3 | 1 2 1 3 2 2 1 4 2 1 1 3 2 2 1
4 | 1 2 1 3 2 2 1 4 2 1 1 3 2 2 1
5 | 1 2 1 3 2 2 1 4 2 1 1 3 2 2 1
6 | 1 2 1 3 2 2 1 4 2 1 1 3 2 2 1
7 | 1 2 1 3 2 2 1 4 2 1 1 3 2 2 1
8 | 1 2 1 3 2 2 1 4 2 1 1 3 2 2 1
9 | 1 2 1 3 2 2 1 4 2 1 1 3 2 2 1
10 | 1 2 1 3 2 2 1 4 2 1 1 3 2 2 1
11 | 1 2 1 3 2 2 1 4 2 1 1 3 2 2 1
12 | 1 2 1 3 2 2 1 4 2 1 1 3 2 2 1
13 | 1 2 1 3 2 2 1 4 2 1 1 3 2 2 1
14 | 1 2 1 3 2 2 1 4 2 1 1 3 2 2 1
15 | 1 2 1 3 2 2 1 4 2 1 1 3 2 2 1
CROSSREFS
Sequence in context: A233548 A080027 A341970 * A220465 A050305 A117164
KEYWORD
nonn,tabl
AUTHOR
STATUS
approved