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A167667
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Expansion of (1-x+4*x^2)/(1-2*x)^2.
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12
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1, 3, 12, 36, 96, 240, 576, 1344, 3072, 6912, 15360, 33792, 73728, 159744, 344064, 737280, 1572864, 3342336, 7077888, 14942208, 31457280, 66060288, 138412032, 289406976, 603979776, 1258291200, 2617245696, 5435817984, 11274289152, 23353884672, 48318382080
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OFFSET
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0,2
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COMMENTS
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Also the number of maximal and maximum cliques in the n-cube-connected cycles graph for n > 3. - Eric W. Weisstein, Dec 01 2017
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LINKS
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FORMULA
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a(0)=1, a(n) = 3*n*2^(n-1) for n>0.
a(0)=1, a(1)=3, a(2)=12, a(n) = 4*a(n-1)-4*a(n-2) for n>2.
a(n) = Sum_{k=0..n} A167666(n,k) * 2^k.
G.f.: 1 + 3*x*G(0)/2, where G(k)= 1 + 1/(1 - x/(x + (k+1)/(2*k+4)/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 01 2013
a(0)=1, a(n) = Sum_{i=0..n} binomial(n,i) * (2n-i). - Wesley Ivan Hurt, Mar 20 2015
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MAPLE
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MATHEMATICA
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CoefficientList[Series[(1 - x + 4*x^2)/(1 - 2*x)^2, {x, 0, 30}], x] (* Wesley Ivan Hurt, Mar 20 2015 *)
Join[{1}, LinearRecurrence[{4, -4}, {3, 12}, 20]] (* Eric W. Weisstein, Dec 01 2017 *)
CoefficientList[Series[(1 - x + 4 x^2)/(-1 + 2 x)^2, {x, 0, 20}], x] (* Eric W. Weisstein, Dec 01 2017 *)
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PROG
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(PARI) Vec((1-x+4*x^2)/(1-2*x)^2 + O(x^50)) \\ Michel Marcus, Mar 21 2015
(PARI) a(n) = if(n==0, 1, 3*n*2^(n-1)); \\ Altug Alkan, May 16 2018
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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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