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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.
4
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
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.
Sequence in context: A226590 A261349 A227962 * A255615 A056931 A139569
KEYWORD
nonn,look,tabf
AUTHOR
Alois P. Heinz, Jan 09 2020
STATUS
approved