A138585 The sequence is formed by concatenating subsequences S1, S2, ... each of finite length. S1 consists of the element 1. The n-th subsequence consist of numbers {(n/2)*(n/2 - 1)+ 1, ..., (n/2)*(n/2 + 1)} for n even, {((n-1)/2)^2, ..., (n-1)/2 * ((n-1)/2 + 2)} for n odd.

1, 1, 2, 1, 2, 3, 3, 4, 5, 6, 4, 5, 6, 7, 8, 7, 8, 9, 10, 11, 12, 9, 10, 11, 12, 13, 14, 15, 13, 14, 15, 16, 17, 18, 19, 20, 16, 17, 18, 19, 20, 21, 22, 23, 24, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 31, 32, 33, 34, 35

Offset: 1

Author

Ctibor O. Zizka, May 13 2008

Keywords

• easy
• nonn

Comments

A generalized Connell sequence.

Except for the first term the first element of each subsequence Sn (equivalently, each row of the triangle) gives A004652 (offset by 1), and the last element is A035106.

Examples

			S1: {1}
S2: {1,2}
S3: {1,2,3,}
S4: {3,4,5,6}
S5: {4,5,6,7,8}
S6: {7,8,9,10,11,12}, etc.
so concatenation of S1/S2/S3/S4/S5/S6/... gives:
1,1,2,1,2,3,3,4,5,6,4,5,6,7,8,7,8,9,10,11,12,...
		

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..10000
• Douglas E. Iannucci and Donna Mills-Taylor. On Generalizing the Connell Sequence. Journal of Integer Sequences 2 (1999), Article 99.1.7.

Crossrefs

Cf. A001614.

Programs

Maple

S := proc(n) local s: if(n=1)then s:=1: elif(n mod 2 = 0)then s:=(n/2)*(n/2 -1)+1: else s:=((n-1)/2)^2: fi: seq(k,k=s..s+n-1): end: seq(S(n),n=1..12); # Nathaniel Johnston, Oct 01 2011

Extensions

Corrected and edited by D. S. McNeil, Dec 12 2010