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A075302
Transpose of array A075300.
4
0, 2, 1, 4, 5, 3, 6, 9, 11, 7, 8, 13, 19, 23, 15, 10, 17, 27, 39, 47, 31, 12, 21, 35, 55, 79, 95, 63, 14, 25, 43, 71, 111, 159, 191, 127, 16, 29, 51, 87, 143, 223, 319, 383, 255, 18, 33, 59, 103, 175, 287, 447, 639, 767, 511, 20, 37, 67, 119, 207, 351, 575, 895, 1279
OFFSET
0,2
COMMENTS
The top-left corner of the array looks like:
0 2 4 6 8 10 12 14 ...
1 5 9 13 17 21 25 29 ...
3 11 19 27 35 43 51 59 ...
7 23 39 55 71 87 ...
15 47 79 ...
This can be used to construct mappings like A059884 and A075173, where the elements of the first row give the bit-positions where to interleave the first element of a finite vector of nonnegative integers, the second row the bit-positions for the second element, etc.
MAPLE
A075302 := n -> A075300bi(A002262(n), A025581(n));
A075300bi := (x, y) -> (2^x * (2*y + 1))-1;
A002262 := n -> n - binomial(floor((1/2)+sqrt(2*(1+n))), 2);
A025581 := n -> binomial(1+floor((1/2)+sqrt(2*(1+n))), 2) - (n+1);
CROSSREFS
Inverse permutation: A075303. Transpose: A075300. The X-projection is given by A025480 and the Y-projection is A007814(n+1). Cf. A002262, A025581.
Sequence in context: A354699 A239806 A330402 * A352520 A350313 A257911
KEYWORD
nonn,tabl
AUTHOR
Antti Karttunen, Sep 12 2002
STATUS
approved