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A114752 a(2n)=2n, a(2n+1)=4n+1. 7
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
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
LINKS
Eric Angelini, k-chunks sum and division by k, post to the SeqFan list, Mar 22 2013.
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
Sequence in context: A214533 A065221 A283419 * A204923 A123302 A227368
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 February 29 16:27 EST 2024. Contains 370425 sequences. (Running on oeis4.)