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A135344
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a(n) = 3*a(n-1) - a(n-3) + 3*a(n-4).
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1
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1, 1, 1, 1, 5, 17, 53, 157, 469, 1405, 4217, 12653, 37961, 113881, 341641, 1024921, 3074765, 9224297, 27672893, 83018677, 249056029, 747168085, 2241504257, 6724512773, 20173538321, 60520614961, 181561844881, 544685534641, 1634056603925, 4902169811777
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OFFSET
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0,5
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LINKS
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FORMULA
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3*a(n) - a(n+1) = hexaperiodic 2, 2, 2, -2, -2, -2 = 2*A130151.
a(n) = (1/14)*3^n + (1/6)*(-1)^n + (16/21)*cos(Pi*n/3) + (8*sqrt(3)/21)*sin(Pi*n/3).
a(n) = (1/14)*3^n + (1/14)*[13; 11; 5; -13; -11; -5]. (End)
G.f.: ( -1+2*x+2*x^2+x^3 ) / ( (3*x-1)*(1+x)*(x^2-x+1) ). - Harvey P. Dale, Apr 15 2012
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MATHEMATICA
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LinearRecurrence[{3, 0, -1, 3}, {1, 1, 1, 1}, 40] (* Harvey P. Dale, Apr 15 2012 *)
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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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