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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).

%I A329278 #29 Jul 14 2023 11:53:39
%S A329278 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,
%T A329278 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,
%U A329278 31,26,22,19,17,16,0,1,3,6,10,15,21,28,36,45,55,2
%N 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).
%C A329278 Conjecture: for n > 0, the n-th row has 2^(n-1)-1 descents.
%C A329278 T(n,k) = A000217(k) for 0 <= k <= A017911(n+1), and T(n,2^n-1) = 2^(n-1).
%H A329278 Peter Kagey, <a href="/A329278/b329278.txt">Table of n, a(n) for n = 0..8190</a> (first 12 rows)
%e A329278 Table begins:
%e A329278   0;
%e A329278   0, 1;
%e A329278   0, 1, 3, 2;
%e A329278   0, 1, 3, 6,  2,  7, 5,  4;
%e A329278   0, 1, 3, 6, 10, 15, 5, 12, 4, 13, 7, 2, 14, 11, 9, 8;
%e A329278   ...
%p A329278 T:= (n, k)-> irem(k*(k+1)/2, 2^n):
%p A329278 seq(seq(T(n, k), k=0..2^n-1), n=0..6);  # _Alois P. Heinz_, Jan 08 2020
%Y A329278 Cf. A000217, A000225, A017911, A053645, A105332, A330766, A331105, A363674.
%Y A329278 T(n,2^n-1) gives A131577.
%K A329278 nonn,tabf,look
%O A329278 0,6
%A A329278 _Peter Kagey_, Nov 11 2019