

A057027


Triangle T read by rows: row n consists of the numbers C(n,2)+1 to C(n+1,2); numbers in oddnumbered places form an increasing sequence and the others a decreasing sequence.


9



1, 2, 3, 4, 6, 5, 7, 10, 8, 9, 11, 15, 12, 14, 13, 16, 21, 17, 20, 18, 19, 22, 28, 23, 27, 24, 26, 25, 29, 36, 30, 35, 31, 34, 32, 33, 37, 45, 38, 44, 39, 43, 40, 42, 41, 46, 55, 47, 54, 48, 53, 49, 52, 50, 51, 56, 66, 57, 65, 58, 64, 59, 63, 60, 62, 61, 67, 78, 68, 77, 69, 76
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OFFSET

1,2


COMMENTS

Arrange the quotients F(i)/F(j) of Fibonacci numbers, for 2<=i<j<=n, in increasing order. Then the positions of the F(i)/F(nk) are the first nk2 terms of the diagonal T(i,ik), for k=0,1,2,...,n3.


LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..10000
Index entries for sequences that are permutations of the natural numbers


EXAMPLE

For n=6, the ordered quotients are 1/8, 1/5, 2/8, 1/3, 3/8, 2/5, 1/2, 3/5, 5/8, 2/3; the positions of 1/5, 2/5, 3/5 are 2, 6, 8 (first terms of diagonal T(i, i1)).
Triangle starts:
1;
2, 3;
4, 6, 5;
7,10, 8, 9;
...


MATHEMATICA

nn= 12; t = Table[Range[Binomial[n, 2] + 1, Binomial[n + 1, 2]], {n, nn}]; Table[t[[n, If[OddQ@ k, Ceiling[k/2], k/2] ]], {n, nn}, {k, n}] // Flatten (* Michael De Vlieger, Jul 02 2016 *)


CROSSREFS

Reflection of the array in A057028 about its central column, a permutation of the natural numbers.
Inverse permutation to A064578. Central column: A057029.
Sequence in context: A064578 A194969 A194981 * A090894 A175004 A191734
Adjacent sequences: A057024 A057025 A057026 * A057028 A057029 A057030


KEYWORD

nonn,tabl


AUTHOR

Clark Kimberling, Jul 28 2000


EXTENSIONS

Corrected and extended by Vladeta Jovovic, Oct 18 2001


STATUS

approved



