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

1,3

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.

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.

Example

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,...

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

Crossrefs

Cf. A001614.

Sequence in context: A323089 A239511 A264052 * A070048 A116498 A143472

Adjacent sequences: A138582 A138583 A138584 * A138586 A138587 A138588

Keyword

easy,nonn

Author

Ctibor O. Zizka, May 13 2008

Extensions

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

Status

approved