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A016129
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Expansion of 1/((1-2x)(1-6x)).
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24
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1, 8, 52, 320, 1936, 11648, 69952, 419840, 2519296, 15116288, 90698752, 544194560, 3265171456, 19591036928, 117546237952, 705277460480, 4231664828416, 25389989101568, 152339934871552, 914039609753600
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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a(n)= A071951(n+2, 2) = 9*(2*3)^(n-1) - (2*1)^(n-1) = (2^(n-1))*(3^(n+1)-1), n>=0. - Wolfdieter Lang, Nov 07 2003
From Lambert Klasen (lambert.klasen(AT)gmx.net), Feb 05 2005: (Start)
G.f.: 1/((1-2*x)*(1-6*x)).
E.g.f.: (-exp(2*x) + 3*exp(6*x))/2.
a(n) = (6^(n+1) - 2^(n+1))/4. (End)
a(n-1) = ((4+sqrt4)^n - (4-sqrt4)^n)/4 in Fibonacci form. - Al Hakanson (hawkuu(AT)gmail.com), Dec 31 2008
a(n) = det(|ps(i+2,j+1)|, 1 <= i,j <= n), where ps(n,k) are Legendre-Stirling numbers of the first kind (A129467). - Mircea Merca, Apr 06 2013
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MATHEMATICA
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CoefficientList[Series[1/((1-2x)(1-6x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{8, -12}, {1, 8}, 30] (* Harvey P. Dale, Jan 15 2015 *)
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PROG
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(Sage) [lucas_number1(n, 8, 12) for n in range(1, 21)] # Zerinvary Lajos, Apr 23 2009
(Sage) [(6^n - 2^n)/4 for n in range(1, 21)] # Zerinvary Lajos, Jun 04 2009
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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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