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A081183
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6th binomial transform of (0,1,0,2,0,4,0,8,0,16,...).
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9
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0, 1, 12, 110, 912, 7204, 55440, 420344, 3159168, 23618320, 176008128, 1309074656, 9724619520, 72186895936, 535605687552, 3972913788800, 29464372088832, 218493396246784, 1620132103941120, 12012809774902784, 89069225764835328
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = 12*a(n-1) - 34*a(n-2) with n > 1, a(0)=0, a(1)=1.
G.f.: x/(1 - 12*x + 34*x^2).
a(n) = ((6 + sqrt(2))^n - (6 - sqrt(2))^n)/(2*sqrt(2)).
a(n) = Sum_{k=0..n} C(n,2k+1)*2^k*6^(n-2k-1).
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MATHEMATICA
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CoefficientList[Series[x / (1 - 12 x + 34 x^2), {x, 0, 20}], x] (* Vincenzo Librandi, Aug 07 2013 *)
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PROG
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(Sage) [lucas_number1(n, 12, 34) for n in range(0, 21)] # Zerinvary Lajos, Apr 27 2009
(Magma) [n le 2 select n-1 else 12*Self(n-1)-34*Self(n-2): n in [1..25] ]; // Vincenzo Librandi, Aug 07 2013
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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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