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A117616
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a(0)=0, a(n)=4a(n-1)+2 for n odd, a(n)=4a(n-1) for n even.
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3
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0, 2, 8, 34, 136, 546, 2184, 8738, 34952, 139810, 559240, 2236962, 8947848, 35791394, 143165576, 572662306, 2290649224, 9162596898, 36650387592, 146601550370, 586406201480, 2345624805922, 9382499223688, 37529996894754
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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+2^(3+2*n))/15. a(n) = 4*a(n-1)+a(n-2)-4*a(n-3). G.f.: 2*x / ((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 0 elif n mod 2 = 1 then 4*a(n-1)+2 else 4*a(n-1) fi end: seq(a(n), n=0..23);
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MATHEMATICA
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b[0] := 0 b[1] := 2 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, 0}, 30][[;; , 2]] (* or *) LinearRecurrence[{4, 1, -4}, {0, 2, 8}, 30] (* Harvey P. Dale, Mar 10 2023 *)
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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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