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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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Last modified November 18 01:16 EST 2017. Contains 294837 sequences.