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0, 12, 24, 72, 192, 528, 1440, 3936, 10752, 29376, 80256, 219264, 599040, 1636608, 4471296, 12215808, 33374208, 91180032, 249108480, 680577024, 1859371008, 5079896064, 13878534144, 37916860416, 103590789120, 283015299072, 773212176384, 2112454950912
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OFFSET
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0,2
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COMMENTS
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The case k=2 in a family of sequences a(n)=G(k,n), G(k,0)=0, G(k,1)=k*(k+4), G(k,n)=k*G(k,n-1)+k*G(k,n-2).
The Binet formula is G(k,n) = (c^n-b^n)*d where d=sqrt(k*(k+4)); c=(k+d)/2; b=(k-d)/2.
The generating functions are k*(k+4)*x/(1-k*x-k*x^2).
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LINKS
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FORMULA
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Binet formula: a(n) = 2*2^n*((-1+3^(1/2))^(-n)-(-1)^n*(1+3^(1/2))^(-n))*3^(1/2) .
G.f.: 12*x/(1-2*x-2*x^2). a(n) = 2*a(n-1)+2*a(n-2).
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MATHEMATICA
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LinearRecurrence[{2, 2}, {0, 12}, 30] (* Harvey P. Dale, Mar 06 2023 *)
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CROSSREFS
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KEYWORD
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nonn,easy,changed
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AUTHOR
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Claudio Peruzzi (claudio.peruzzi(AT)gmail.com), Jan 22 2010
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EXTENSIONS
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STATUS
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approved
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