A329278 Irregular table read by rows. The n-th row is the permutation of {0, 1, 2, ..., 2^n-1} given by T(n,k) = k(k+1)/2 (mod 2^n).

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

Offset: 0

Author

Peter Kagey, Nov 11 2019

Keywords

• nonn
• tabf
• look

Comments

Conjecture: for n > 0, the n-th row has 2^(n-1)-1 descents.

T(n,k) = A000217(k) for 0 <= k <= A017911(n+1), and T(n,2^n-1) = 2^(n-1).

Examples

			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;
  ...
		

Links

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

Crossrefs

Cf. A000217, A000225, A017911, A053645, A105332, A330766, A331105, A363674.

T(n,2^n-1) gives A131577.

Programs

Maple

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