STATUS
proposed
approved
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Revision History for A339674
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Irregular triangle T(n, k), n, k >= 0, read by rows; for any number m with runs in binary expansion (r_1, ..., r_j), let R(m) = {r_1 + ... + r_j, r_2 + ... + r_j, ..., r_j}; row n corresponds to the numbers k such that R(k) is included in R(n), in ascending order.
(history; published version)
(history; published version)
STATUS
editing
proposed
LINKS
Rémy Sigrist, <a href="/A339674/b339674.txt">Table of n, a(n) for n = 0..6560</a>
STATUS
approved
editing
STATUS
proposed
approved
STATUS
editing
proposed
LINKS
Rémy Sigrist, <a href="/A339674/a339674.png">Scatterplot of (n, T(n, k)) for n <= 2^10</a>
NAME
allocated Irregular triangle T(n, k), n, k >= 0, read by rows; for Rémy Sigristany number m with runs in binary expansion (r_1, ..., r_j), let R(m) = {r_1 + ... + r_j, r_2 + ... + r_j, ..., r_j}; row n corresponds to the numbers k such that R(k) is included in R(n), in ascending order.
DATA
0, 0, 1, 0, 1, 2, 3, 0, 3, 0, 3, 4, 7, 0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 6, 7, 0, 7, 0, 7, 8, 15, 0, 1, 6, 7, 8, 9, 14, 15, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 0, 3, 4, 7, 8, 11, 12, 15, 0, 3, 12, 15, 0, 1, 2, 3, 12, 13, 14, 15, 0, 1, 14, 15, 0
OFFSET
0,6
COMMENTS
For any m > 0, R(m) contains the partial sums of the m-th row of A227736; by convention, R(0) = {}.
The underlying idea is to take some or all of the rightmost runs of a number, and possibly merge some of them.
For any n >= 0, the n-th row:
- has 2^A000120(A003188(n)) terms,
- has first term 0 and last term A003817(n),
- has n at position A090079(n),
- corresponds to the distinct terms in n-th row of table A341840.
EXAMPLE
The triangle starts:
0;
0, 1;
0, 1, 2, 3;
0, 3;
0, 3, 4, 7;
0, 1, 2, 3, 4, 5, 6, 7;
0, 1, 6, 7;
0, 7;
0, 7, 8, 15;
0, 1, 6, 7, 8, 9, 14, 15;
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15;
0, 3, 4, 7, 8, 11, 12, 15;
0, 3, 12, 15;
0, 1, 2, 3, 12, 13, 14, 15;
0, 1, 14, 15;
0, 15;
...
PROG
(PARI) See Links section.
KEYWORD
allocated
nonn,base,tabf
AUTHOR
Rémy Sigrist, Feb 21 2021
STATUS
approved
editing
NAME
allocated for Rémy Sigrist
KEYWORD
recycled
allocated