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 A114752 a(2n)=2n, a(2n+1)=4n+1. 5
 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, 26, 53, 28, 57, 30, 61, 32, 65, 34, 69, 36, 73, 38, 77, 40, 81, 42, 85, 44, 89, 46, 93, 48, 97, 50, 101, 52, 105, 54, 109, 56, 113, 58, 117, 60, 121, 62, 125, 64, 129, 66, 133, 68, 137 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. Equals A133566 * [1,2,3,...]. - Gary W. Adamson, Sep 16 2007 The sequence satisfies a divisibility property described by E. Angelini on the SeqFan list, cf. link. - M. F. Hasler, Mar 22 2013 LINKS Harvey P. Dale, Table of n, a(n) for n = 1..1000 E. Angelini, k-chunks sum and division by k, post to the SeqFan list, Mar 22 2013 Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1). FORMULA a(2n) = 2n, a(2n+1) = 4n+1. - Joshua Zucker, May 05 2006 G.f.: x*(1+2*x+3*x^2)/(1-x^2)^2. - Philippe Deléham, Mar 02 2012 a(n) = (3n-(n-1)(-1)^n-1)/2. - Bruno Berselli, Mar 02 2012 EXAMPLE Contribution by M. F. Hasler, Mar 22 2013: (Start) The triangle described in the original definition starts 1 3 2 3 4 5 7 6 5 4 5 6 7 8 9 11 10 9 8 7 6. (End) MATHEMATICA With[{nn=40}, Riffle[Range[1, 4nn, 4], Range[2, 2nn, 2]]] (* Harvey P. Dale, Apr 14 2017 *) PROG (PARI) a(n)=n+if(n%2, n\2*2) \\ Charles R Greathouse IV, Oct 16 2015 CROSSREFS Cf. A114751, A114753, A133566. Sequence in context: A214533 A065221 A283419 * A204923 A123302 A227368 Adjacent sequences:  A114749 A114750 A114751 * A114753 A114754 A114755 KEYWORD nonn,easy AUTHOR Amarnath Murthy, Nov 15 2005 EXTENSIONS More terms from Joshua Zucker, May 05 2006 Simpler definition from M. F. Hasler, Mar 22 2013 STATUS approved

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