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A078904
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a(n) = 4a(n-1) + 3n with a(0) = 0.
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2
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0, 3, 18, 81, 336, 1359, 5454, 21837, 87372, 349515, 1398090, 5592393, 22369608, 89478471, 357913926, 1431655749, 5726623044, 22906492227, 91625968962, 366503875905, 1466015503680, 5864062014783, 23456248059198, 93824992236861
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: A(x) = -3x/(4x^3 - 9x^2 + 6x - 1).
a(n) = (1/3)*(4^(n+1) - 3*n - 4).
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MAPLE
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a:=n->sum (4^j-1, j=1..n): seq(a(n), n=0..23); # Zerinvary Lajos, Jun 27 2007
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MATHEMATICA
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PROG
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(PARI) a(n)=(1/3)*(4^(n+1)-3*n-4)
(Sage) [gaussian_binomial(n, 1, 4)-n for n in range(1, 25)] # Zerinvary Lajos, May 29 2009
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CROSSREFS
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Max ( Fr(n, k) : 1<=k<=4^(n+1)-3) where Fr(x, y) is defined in A078903.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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