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Search: id:A078904
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| A078904 |
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a(n) = 4a(n-1)+3n with a(0) = 0. |
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+0
3
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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
(list; graph; listen)
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OFFSET
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0,2
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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)
a(n)=3*A014825(n) - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 27 2007
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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 (zerinvarylajos(AT)yahoo.com), Jun 27 2007
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MATHEMATICA
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s=0; lst={}; Do[s+=2^n-1; AppendTo[lst, s], {n, 0, 6!, 2}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 07 2008]
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PROGRAM
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(PARI) a(n)=(1/3)*(4^(n+1)-3*n-4)
(Other) sage: [gaussian_binomial(n, 1, 4)-n for n in xrange(1, 25)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 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.
Sequence in context: A135371 A086346 A036290 this_sequence A099012 A122069 A103897
Adjacent sequences: A078901 A078902 A078903 this_sequence A078905 A078906 A078907
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Dec 12 2002
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EXTENSIONS
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Additional formulae from Ralf Stephan (ralf(AT)ark.in-berlin.de), Dec 19 2002
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