login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A261038 a(1)=1; for n>1: a(n) = a(n-1)*n if t=0, a(n) = round(a(n-1)/n) if t=1, a(n) = a(n-1)+n if t=2, a(n) = a(n-1)-n if t=3, where t = n mod 4. 1
1, 3, 0, 0, 0, 6, -1, -8, -1, 9, -2, -24, -2, 12, -3, -48, -3, 15, -4, -80, -4, 18, -5, -120, -5, 21, -6, -168, -6, 24, -7, -224, -7, 27, -8, -288, -8, 30, -9, -360, -9, 33, -10, -440, -10, 36, -11, -528, -11, 39, -12, -624, -12, 42, -13, -728, -13, 45, -14 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(4*n+1) = 1, 0, -1, -2, -3, ...

a(4*n+2) = 3, 6, 9, 12, 15, ...

a(4*n+3) = 0, -1, -2, -3, -4, ...

a(4*n+4) = 0, -8, -24, -48, -80, ... = -A033996(n).

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (0,0,0,3,0,0,0,-3,0,0,0,1).

FORMULA

From Colin Barker, Aug 09 2015: (Start)

a(n) = 3*a(n-4) - 3*a(n-8) + a(n-12).

G.f.: -x*(x^10+2*x^8-8*x^7-x^6-3*x^5-3*x^4+3*x+1) / ((x-1)^3*(x+1)^3*(x^2+1)^3).

(End)

EXAMPLE

a(1) = 1.

a(2) = a(1) + 2 = 3.

a(3) = a(2) - 3 = 0.

a(4) = a(3) * 4 = 0.

a(5) = round(a(4) / 5) = 0.

a(6) = a(5) + 6 = 6.

a(7) = a(6) - 7 = -1.

MAPLE

a:= proc(n) option remember; `if`(n=1, 1, (t->

`if`(t=0, a(n-1)*n, `if`(t=1, round(a(n-1)/n),

`if`(t=2, a(n-1)+n, a(n-1)-n))))(irem(n, 4)))

end:

seq(a(n), n=1..100); # Alois P. Heinz, Aug 08 2015

MATHEMATICA

nxt[{n_, a_}]:=Module[{t=Mod[n+1, 4]}, {n+1, Which[t==0, a(n+1), t==1, Round[ a/(n+1)], t==2, a+n+1, t==3, a-n-1]}]; NestList[nxt, {1, 1}, 100][[All, 2]] (* or *) LinearRecurrence[{0, 0, 0, 3, 0, 0, 0, -3, 0, 0, 0, 1}, {1, 3, 0, 0, 0, 6, -1, -8, -1, 9, -2, -24}, 100] (* Harvey P. Dale, May 25 2018 *)

PROG

(PARI) Vec(-x*(x^10+2*x^8-8*x^7-x^6-3*x^5-3*x^4+3*x+1)/((x-1)^3*(x+1)^3*(x^2+1)^3) + O(x^100)) \\ Colin Barker, Aug 10 2015

(PARI) first(m)=my(v=vector(m), t); v[1]=1; for(i=2, m, t = i%4; if(t==0, v[i]=v[i-1]*i, if(t==1, v[i]=round(v[i-1]/i), if(t==2, v[i]=v[i-1]+i, v[i]=v[i-1]-i )))); v; \\ Anders Hellström, Aug 17 2015

CROSSREFS

Cf. A033996.

Sequence in context: A327889 A221702 A084681 * A285852 A096528 A161837

Adjacent sequences: A261035 A261036 A261037 * A261039 A261040 A261041

KEYWORD

sign,easy

AUTHOR

Peter Woodward, Aug 07 2015

EXTENSIONS

More terms from Alois P. Heinz, Aug 08 2015

Edited by Jon E. Schoenfield, Aug 08 2015

Corrected by Harvey P. Dale, May 25 2018

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 9 10:28 EST 2022. Contains 358700 sequences. (Running on oeis4.)