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A261038
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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.
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1
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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
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OFFSET
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1,2
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COMMENTS
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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).
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0,0,0,3,0,0,0,-3,0,0,0,1).
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FORMULA
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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)
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EXAMPLE
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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.
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MAPLE
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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:
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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