

A329278


Irregular table read by rows. The nth row is the permutation of {0, 1, 2, ..., 2^n1} given by T(n,k) = k(k+1)/2 (mod 2^n).


3



0, 0, 1, 0, 1, 3, 2, 0, 1, 3, 6, 2, 7, 5, 4, 0, 1, 3, 6, 10, 15, 5, 12, 4, 13, 7, 2, 14, 11, 9, 8, 0, 1, 3, 6, 10, 15, 21, 28, 4, 13, 23, 2, 14, 27, 9, 24, 8, 25, 11, 30, 18, 7, 29, 20, 12, 5, 31, 26, 22, 19, 17, 16, 0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 2
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OFFSET

0,6


COMMENTS

Conjecture: for n > 0, the nth row has 2^(n1)1 descents.
T(n,k) = A000217(k) for 0 <= k <= A017911(n+1), and T(n,2^n1) = 2^(n1).


LINKS

Peter Kagey, Table of n, a(n) for n = 0..8190 (first 12 rows)


EXAMPLE

Table begins:
0;
0, 1;
0, 1, 3, 2;
0, 1, 3, 6, 2, 7, 5, 4;
0, 1, 3, 6, 10, 15, 5, 12, 4, 13, 7, 2, 14, 11, 9, 8;
...


MAPLE

T:= (n, k)> irem(k*(k+1)/2, 2^n):
seq(seq(T(n, k), k=0..2^n1), n=0..6); # Alois P. Heinz, Jan 08 2020


CROSSREFS

Cf. A000217, A000225, A017911, A053645, A105332, A330766, A331105.
T(n,2^n1) gives A131577.
Sequence in context: A079618 A151844 A286223 * A008783 A139144 A081576
Adjacent sequences: A329275 A329276 A329277 * A329279 A329280 A329281


KEYWORD

nonn,tabf,look


AUTHOR

Peter Kagey, Nov 11 2019


STATUS

approved



