A057028 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 a decreasing sequence and the others an increasing sequence.

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

Offset: 1

Author

Clark Kimberling, Jul 28 2000

Keywords

• nonn
• tabl

Examples

			Rows: 1; 3,2; 5,6,4; 9,8,10,7; ...
		

Links

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

Crossrefs

Reflection of the array in A057027 about its central column, a permutation of the natural numbers.

Inverse permutation: A064789.

Programs

Mathematica

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