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A081199
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5th binomial transform of (0,1,0,1,...), A000035.
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8
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0, 1, 10, 76, 520, 3376, 21280, 131776, 807040, 4907776, 29708800, 179301376, 1080002560, 6496792576, 39047864320, 234555621376, 1408407470080, 8454739787776, 50745618595840, 304542431051776, 1827529464217600
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OFFSET
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0,3
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COMMENTS
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Conjecture (verified up to a(9)): Number of collinear 4-tuples of points in a 4 X 4 X 4 X ... n-dimensional cubic grid. - R. H. Hardin, May 24 2010
a(n) is also the total number of words of length n, over an alphabet of six letters, of which one of them appears an odd number of times. See a Lekraj Beedassy, Jul 22 2003, comment on A006516 (4-letter case), and the Balakrishnan reference there. For the 2-, 3-, 5- and 7-letter case analogs see A131577, A003462, A005059 and A081200, respectively. - Wolfdieter Lang, Jul 16 2017
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LINKS
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FORMULA
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a(n) = 10*a(n-1) - 24*a(n-2) with n>1, a(0)=0, a(1)=1.
G.f.: x/((1-4*x)*(1-6*x)).
a(n) = 6^n/2 - 4^n/2.
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MAPLE
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seq(add(2^(2*n-k)*binomial(n, k)/2, k=1..n), n=0..20); # Zerinvary Lajos, Apr 18 2009
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MATHEMATICA
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CoefficientList[Series[x / ((1 - 4 x) (1 - 6 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Aug 07 2013 *)
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PROG
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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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