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Irregular triangle T(n, k), n >= 0, k = 1..2^A092339(n), read by rows; the n-th row lists the numbers k such that n appears in the k-th row of A361644.
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%I #11 Mar 21 2023 15:03:39

%S 0,1,2,2,3,4,5,5,5,6,4,5,6,7,8,9,10,11,9,10,10,10,11,10,11,12,13,10,

%T 13,9,10,13,14,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,17,18,21,

%U 22,18,21,18,19,20,21,20,21,21,21,22,20,21,22,23,20,21,22,23,24,25,26,27

%N Irregular triangle T(n, k), n >= 0, k = 1..2^A092339(n), read by rows; the n-th row lists the numbers k such that n appears in the k-th row of A361644.

%C In other words, the n-th row contains the numbers k with the same binary length as n and for any i >= 0, if the i-th bit and the (i+1)-th bit in n are different then they are also different in k (i = 0 corresponding to the least significant bit).

%H Rémy Sigrist, <a href="/A361674/b361674.txt">Table of n, a(n) for n = 0..9841</a> (rows for n = 0..511 flattened)

%F T(n, 1) = A361645(n).

%F T(n, 2^A092339(n)) = A361676(n).

%e Triangle T(n, k) begins (in decimal and in binary):

%e n n-th row bin(n) n-th row in binary

%e -- -------------- ------ ----------------------

%e 0 0 0 0

%e 1 1 1 1

%e 2 2 10 10

%e 3 2, 3 11 10, 11

%e 4 4, 5 100 100, 101

%e 5 5 101 101

%e 6 5, 6 110 101, 110

%e 7 4, 5, 6, 7 111 100, 101, 110, 111

%e 8 8, 9, 10, 11 1000 1000, 1001, 1010, 1011

%e 9 9, 10 1001 1001, 1010

%e 10 10 1010 1010

%e 11 10, 11 1011 1010, 1011

%e 12 10, 11, 12, 13 1100 1010, 1011, 1100, 1101

%e 13 10, 13 1101 1010, 1101

%e 14 9, 10, 13, 14 1110 1001, 1010, 1101, 1110

%o (PARI) row(n) = { my (r = [n], m); for (e = 1, exponent(n), if (bittest(n, e-1)==bittest(n, e), m = 2^e-1; r = concat(r, [bitxor(v, m) | v <- r]););); vecsort(r); }

%Y Cf. A361644, A361645, A361676.

%K nonn,base,tabf

%O 0,3

%A _Rémy Sigrist_, Mar 20 2023