A114752 a(2n)=2n, a(2n+1)=4n+1.

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

Offset: 1

Author

Amarnath Murthy, Nov 15 2005

Keywords

• nonn
• easy

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

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

Examples

			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)
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Eric 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).

Crossrefs

Cf. A114751, A114753, A133566, A014255

Programs

Mathematica

With[{nn=40},Riffle[Range[1,4nn,4],Range[2,2nn,2]]] (* Harvey P. Dale, Apr 14 2017 *)

PARI

a(n)=n+if(n%2,n\2*2) \\ Charles R Greathouse IV, Oct 16 2015

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

Extensions

More terms from Joshua Zucker, May 05 2006

Simpler definition from M. F. Hasler, Mar 22 2013