A359941 Irregular triangle read row by row. The k-th row are integers from 0 to 2^k-1 in base 2 ordered in graded reverse lexicographical order.
0, 0, 1, 0, 1, 2, 3, 0, 1, 2, 4, 3, 5, 6, 7, 0, 1, 2, 4, 8, 3, 5, 9, 6, 10, 12, 7, 11, 13, 14, 15, 0, 1, 2, 4, 8, 16, 3, 5, 9, 17, 6, 10, 18, 12, 20, 24, 7, 11, 19, 13, 21, 25, 14, 22, 26, 28, 15, 23, 27, 29, 30, 31, 0, 1, 2, 4, 8, 16, 32, 3, 5, 9, 17, 33, 6
Offset: 0
Examples
As an irregular triangle: 0; 0, 1; 0, 1, 2, 3; 0, 1, 2, 4, 3, 5, 6, 7; 0, 1, 2, 4, 8, 3, 5, 9, 6, 10, 12, 7, 11, 13, 14, 15; ... For k = 4, the graded lexicographical order of integers 0..15 written in base 2 is 0000 0001, 0010, 0100, 1000, 0011, 0101, 1001, 0110, 1010, 1100, 0111, 1011, 1101, 1110, 1111 Note that 1001 < 0110 as the least significant digit on which they differ is the last one, and 1 < 0 due to the reverse colexicographical ordering.
Links
- Alois P. Heinz, Rows n = 0..13, flattened
- Jean Liénardy, C++ program
- Wikipedia, Monomial order
Programs
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Maple
T:= n-> map(x-> add(2^(i-1), i=x), [seq( combinat[choose]([$1..n], i)[], i=0..n)])[]: seq(T(n), n=0..6); # Alois P. Heinz, Feb 03 2023
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