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A077834
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Expansion of 1/(1 - 2*x - 2*x^2 - 3*x^3).
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3
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1, 2, 6, 19, 56, 168, 505, 1514, 4542, 13627, 40880, 122640, 367921, 1103762, 3311286, 9933859, 29801576, 89404728, 268214185, 804642554, 2413927662, 7241782987, 21725348960, 65176046880, 195528140641, 586584421922, 1759753265766, 5279259797299, 15837779391896
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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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G.f.: 1/((1-3*x)(1 + x + x^2)).
a(n) = sum_{k=0..n} (3^k*2*sqrt(3)*cos(2*Pi*(n-k)/3 + Pi/6)/3).
a(n) = 3^(n+2)/13 + 2*sqrt(3)*cos(2*Pi*n/3 + Pi/6)/39 + 2*sqrt(3)*sin(2*Pi*n/3 + Pi/3)/13.
(End)
a(0)=1, a(1)=2, a(2)=6, a(n) = 2*a(n-1) + 2*a(n-2) + 3*a(n-3). - Harvey P. Dale, Jan 31 2012
a(n) = 1/52*(4*3^(n + 2) + (-1)^n*(2*(-1)^floor(n/3) + 9*(-1)^floor((1 + n)/3) + 6*(-1)^floor((n + 2)/3) + (-1)^floor((n + 4)/3))). - John M. Campbell, Dec 23 2016
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MAPLE
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A049347 := proc(n) op(1+(n mod 3), [1, -1, 0]) ; end proc:
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MATHEMATICA
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CoefficientList[Series[1/(1-2x-2x^2-3x^3), {x, 0, 30}], x] (* or *) LinearRecurrence[{2, 2, 3}, {1, 2, 6}, 30] (* Harvey P. Dale, Jan 31 2012 *)
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PROG
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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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STATUS
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approved
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