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A117614
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a(0)=1, a(n)=4a(n-1)+2 for n odd, a(n)=4a(n-1) for n even.
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1
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1, 6, 24, 98, 392, 1570, 6280, 25122, 100488, 401954, 1607816, 6431266, 25725064, 102900258, 411601032, 1646404130, 6585616520, 26342466082, 105369864328, 421479457314, 1685917829256, 6743671317026, 26974685268104
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OFFSET
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0,2
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REFERENCES
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L. Rosenfeld, Nuclear Forces, section II, Interscience, New York, 1948, p 202.
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LINKS
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FORMULA
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a(n) = (-5-3*(-1)^n+23*4^n)/15. a(n) = 4*a(n-1)+a(n-2)-4*a(n-3). G.f.: -(x^2-2*x-1) / ((x-1)*(x+1)*(4*x-1)). [Colin Barker, Feb 17 2013]
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MAPLE
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a:=proc(n) if n=0 then 1 elif n mod 2 = 1 then 4*a(n-1)+2 else 4*a(n-1) fi end: seq(a(n), n=0..25);
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MATHEMATICA
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b[0] := 1 b[1] := 6 b[n_?EvenQ] := b[n] = 4*b[n - 1] b[n_?OddQ] := b[n] = 4*b[n - 1] + 2 a = Table[b[n], {n, 0, 25}]
nxt[{n_, a_}]:={n+1, If[EvenQ[n], 4a+2, 4a]}; NestList[nxt, {0, 1}, 30][[All, 2]] (* or *) LinearRecurrence[{4, 1, -4}, {1, 6, 24}, 30] (* Harvey P. Dale, Nov 15 2020 *)
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CROSSREFS
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KEYWORD
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nonn,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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