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%I #32 Jan 02 2023 12:30:46
%S 1,2,5,4,9,6,13,8,17,10,21,12,25,14,29,16,33,18,37,20,41,22,45,24,49,
%T 26,53,28,57,30,61,32,65,34,69,36,73,38,77,40,81,42,85,44,89,46,93,48,
%U 97,50,101,52,105,54,109,56,113,58,117,60,121,62,125,64,129,66,133,68,137
%N a(2n)=2n, a(2n+1)=4n+1.
%C Original definition (typos corrected): The following triangle contains n consecutive numbers beginning from n in ascending order if n is odd else in descending order. 1 3 2 3 4 5 7 6 5 4 5 6 7 8 9 11 10 9 8 7 6 ... Sequence contains the leading diagonal.
%C Equals A133566 * [1,2,3,...]. - _Gary W. Adamson_, Sep 16 2007
%C The sequence satisfies a divisibility property described by E. Angelini on the SeqFan list, cf. link. - _M. F. Hasler_, Mar 22 2013
%C First difference of A014255 (shown easily from the Nurikabe property of that sequence, or by manipulating the linear recurrence representations). - _Allan C. Wechsler_, Oct 20 2022
%H Harvey P. Dale, <a href="/A114752/b114752.txt">Table of n, a(n) for n = 1..1000</a>
%H Eric Angelini, <a href="http://list.seqfan.eu/oldermail/seqfan/2013-March/010956.html">k-chunks sum and division by k</a>, post to the SeqFan list, Mar 22 2013.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,0,-1).
%F a(2n) = 2n, a(2n+1) = 4n+1. - _Joshua Zucker_, May 05 2006
%F G.f.: x*(1+2*x+3*x^2)/(1-x^2)^2. - _Philippe Deléham_, Mar 02 2012
%F a(n) = (3n-(n-1)*(-1)^n-1)/2. - _Bruno Berselli_, Mar 02 2012
%e Contribution by _M. F. Hasler_, Mar 22 2013: (Start)
%e The triangle described in the original definition starts
%e 1
%e 3 2
%e 3 4 5
%e 7 6 5 4
%e 5 6 7 8 9
%e 11 10 9 8 7 6. (End)
%t With[{nn=40},Riffle[Range[1,4nn,4],Range[2,2nn,2]]] (* _Harvey P. Dale_, Apr 14 2017 *)
%o (PARI) a(n)=n+if(n%2,n\2*2) \\ _Charles R Greathouse IV_, Oct 16 2015
%Y Cf. A114751, A114753, A133566, A014255
%K nonn,easy
%O 1,2
%A _Amarnath Murthy_, Nov 15 2005
%E More terms from _Joshua Zucker_, May 05 2006
%E Simpler definition from _M. F. Hasler_, Mar 22 2013
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