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, 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
Offset: 1
Examples
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.
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).
Crossrefs
Cf. A033996.
Programs
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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 *) -
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
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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
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)
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
Comments