login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A116966 a(n) = n + {1,2,0,1} according as n == {0,1,2,3} mod 4. 11
1, 3, 2, 4, 5, 7, 6, 8, 9, 11, 10, 12, 13, 15, 14, 16, 17, 19, 18, 20, 21, 23, 22, 24, 25, 27, 26, 28, 29, 31, 30, 32, 33, 35, 34, 36, 37, 39, 38, 40, 41, 43, 42, 44, 45, 47, 46, 48, 49, 51, 50, 52, 53, 55, 54, 56, 57, 59, 58, 60, 61, 63, 62, 64, 65, 67, 66, 68 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

In each group of four consecutive numbers, swap 2nd and 3rd terms. - Zak Seidov, Mar 31 2006

First differences of A089781. - Reinhard Zumkeller, Aug 15 2015

From Guenther Schrack, May 31 2017: (Start)

Permutation of the positive integers partitioned into quadruples [4k+1,4k+3,4k+2,4k+4].

Partial sums: A116996. (End)

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

FORMULA

a(n) = n+1+(i^(n(n-1))-(-1)^n)/2, where i=sqrt(-1). - Bruno Berselli, Nov 25 2012

G.f.: (2*x^3-x^2+2*x+1) / ((x-1)^2*(x+1)*(x^2+1)). - Colin Barker, Apr 30 2013

a(n) = A140081(n+2) + n. - Reinhard Zumkeller, Aug 15 2015

From Guenther Schrack, May 31 2017: (Start)

a(n) = n + 1 + ((-1)^(n*(n-1)/2) - (-1)^n)/2.

a(n) = a(n-4) + 4, n > 3.

a(n) = a(n-1) + a(n-4) - a(n-5), n > 4. (End)

MAPLE

f:=proc(i) if i mod 4 = 0 then i+1 elif i mod 4 = 1 then i+2 elif i mod 4 = 2 then i else i+1; fi; end;

MATHEMATICA

b := {1, 2, 0, 1}; a[n_] := n + b[[1 + Mod[n, 4]]]; Table[a[n], {n, 0, 60}] (* Stefan Steinerberger, Mar 31 2006 *)

CoefficientList[Series[(2 x^3 - x^2 + 2 x + 1) / ((x - 1)^2 (x + 1) (x^2 + 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 19 2013 *)

PROG

(Maxima) makelist(n+1+(%i^(n*(n-1))-(-1)^n)/2, n, 0, 70); \\ Bruno Berselli, Nov 25 2012

(MAGMA) /* By definition: */ [ n + [1, 2, 0, 1][1+(n mod 4)]: n in [0..70] ]; // Bruno Berselli, Nov 25 2012

(PARI) Vec((2*x^3-x^2+2*x+1) / ((x-1)^2*(x+1)*(x^2+1)) + O(x^66) ) \\ Joerg Arndt, Apr 30 2013

(Haskell)

a116966 n = a116966_list !! n

a116966_list = zipWith (+) [0..] $ drop 2 a140081_list

-- Reinhard Zumkeller, Aug 15 2015

CROSSREFS

Cf. A115391.

Cf. A140081, A089781.

Sequence in context: A039906 A056011 A117123 * A182187 A163241 A234027

Adjacent sequences:  A116963 A116964 A116965 * A116967 A116968 A116969

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Mar 31 2006

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 15 03:48 EST 2019. Contains 329990 sequences. (Running on oeis4.)