

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, kchunks 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)/(1x^2)^2.  Philippe Deléham, Mar 02 2012
a(n) = (3n(n1)(1)^n1)/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



