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A123208
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Start with 1, then alternately add 2 or double.
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6
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1, 3, 6, 8, 16, 18, 36, 38, 76, 78, 156, 158, 316, 318, 636, 638, 1276, 1278, 2556, 2558, 5116, 5118, 10236, 10238, 20476, 20478, 40956, 40958, 81916, 81918, 163836, 163838, 327676, 327678, 655356, 655358, 1310716, 1310718, 2621436, 2621438, 5242876, 5242878
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OFFSET
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0,2
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LINKS
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FORMULA
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a(2n) = 5*2^n - 4; a(2n+1) = 5*2^n - 2 (n >= 0). - Emeric Deutsch, Oct 10 2006
a(n) = 3*a(n-2) - 2*a(n-4).
G.f.: (1+3*x+3*x^2-x^3)/((1-x)*(1+x)*(1-2*x^2)). (End)
E.g.f.: 5*cosh(sqrt(2)*x) - 4*cosh(x) + 5*sinh(sqrt(2)*x)/sqrt(2) - 2*sinh(x). - Stefano Spezia, Oct 03 2023
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EXAMPLE
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1, 1+2=3, 3*2=6, 6+2=8, 8*2=16, ...
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MAPLE
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a:=proc(n) if n mod 2 = 0 then 5*2^(n/2)-4 else 5*2^((n-1)/2)-2 fi end: seq(a(n), n=0..45); # Emeric Deutsch, Oct 10 2006
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MATHEMATICA
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nxt[{a_, b_}]:={b+2, 2(b+2)}; Rest[Flatten[NestList[nxt, {1, 1}, 20]]] (* or *) LinearRecurrence[{0, 3, 0, -2}, {1, 3, 6, 8}, 40] (* Harvey P. Dale, Oct 10 2012 *)
CoefficientList[Series[(1 + 3 x + 3 x^2 - x^3) / ((1 - x) (1 + x) (1 - 2 x^2)), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 25 2013 *)
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PROG
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(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1+3*x+3*x^2-x^3)/((1-x^2)*(1-2*x^2)))); // Vincenzo Librandi, Jun 25 2013
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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