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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.

%I A138585 #15 May 04 2019 21:49:35
%S A138585 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,
%T A138585 14,15,16,17,18,19,20,16,17,18,19,20,21,22,23,24,21,22,23,24,25,26,27,
%U A138585 28,29,30,25,26,27,28,29,30,31,32,33,34,35,31,32,33,34,35
%N 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.
%C A138585 A generalized Connell sequence.
%C A138585 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.
%H A138585 Nathaniel Johnston, <a href="/A138585/b138585.txt">Table of n, a(n) for n = 1..10000</a>
%H A138585 Douglas E. Iannucci and Donna Mills-Taylor. <a href="http://www.cs.uwaterloo.ca/journals/JIS/IANN/iann1.html">On Generalizing the Connell Sequence</a>. Journal of Integer Sequences 2 (1999), Article 99.1.7.
%e A138585 S1: {1}
%e A138585 S2: {1,2}
%e A138585 S3: {1,2,3,}
%e A138585 S4: {3,4,5,6}
%e A138585 S5: {4,5,6,7,8}
%e A138585 S6: {7,8,9,10,11,12}, etc.
%e A138585 so concatenation of S1/S2/S3/S4/S5/S6/... gives:
%e A138585 1,1,2,1,2,3,3,4,5,6,4,5,6,7,8,7,8,9,10,11,12,...
%p A138585 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
%Y A138585 Cf. A001614.
%K A138585 easy,nonn
%O A138585 1,3
%A A138585 _Ctibor O. Zizka_, May 13 2008
%E A138585 Corrected and edited by _D. S. McNeil_, Dec 12 2010