A057027 Triangle T read by rows: row n consists of the numbers C(n,2)+1 to C(n+1,2); numbers in odd-numbered places form an increasing sequence and the others a decreasing sequence.

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

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(n-k) are the first n-k-2 terms of the diagonal T(i,i-k), for k=0,1,2,...,n-3.

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, i-1)).
 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: A361251 A194969 A194981 * A371246 A090894 A371360

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