A331105 T(n,k) = -k*(k+1)/2 mod 2^n; triangle T(n,k), n>=0, 0<=k<=2^n-1, read by rows.

0, 0, 1, 0, 3, 1, 2, 0, 7, 5, 2, 6, 1, 3, 4, 0, 15, 13, 10, 6, 1, 11, 4, 12, 3, 9, 14, 2, 5, 7, 8, 0, 31, 29, 26, 22, 17, 11, 4, 28, 19, 9, 30, 18, 5, 23, 8, 24, 7, 21, 2, 14, 25, 3, 12, 20, 27, 1, 6, 10, 13, 15, 16, 0, 63, 61, 58, 54, 49, 43, 36, 28, 19, 9

Offset

0,5

Comments

Row n is a permutation of {0, 1, ..., A000225(n)}.

Links

Alois P. Heinz, Rows n = 0..15, flattened

Example

Triangle T(n,k) begins:
  0;
  0,  1;
  0,  3,  1,  2;
  0,  7,  5,  2, 6, 1,  3, 4;
  0, 15, 13, 10, 6, 1, 11, 4, 12, 3, 9, 14, 2, 5, 7, 8;
  ...

Maple

T:= n-> (p-> seq(modp(-k*(k+1)/2, p), k=0..p-1))(2^n):
seq(T(n), n=0..6);
# second Maple program:
T:= proc(n, k) option remember;
      `if`(k=0, 0, T(n, k-1)-k mod 2^n)
    end:
seq(seq(T(n, k), k=0..2^n-1), n=0..6);

Mathematica

T[n_, k_] := T[n, k] = If[k == 0, 0, Mod[T[n, k - 1] - k, 2^n]];
Table[Table[T[n, k], {k, 0, 2^n - 1}], {n, 0, 6}] // Flatten (* Jean-François Alcover, Mar 28 2022, after Alois P. Heinz *)

Crossrefs

Columns k=0-2 give: A000004, A000225, A036563 (for n>1).

Row sums give A006516.

Row lengths give A000079.

T(n,n) gives A014833 (for n>0).

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

Cf. A329278, A363674.

Sequence in context: A226590 A261349 A227962 * A255615 A056931 A139569

Adjacent sequences: A331102 A331103 A331104 * A331106 A331107 A331108

Keyword

nonn,look,tabf

Author

Alois P. Heinz, Jan 09 2020

Status

approved