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Search: id:A005062
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| 0, 1, 11, 91, 671, 4651, 31031, 201811, 1288991, 8124571, 50700551, 313968931, 1932641711, 11839990891, 72260648471, 439667406451, 2668522016831, 16163719991611, 97745259402791, 590286253682371
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OFFSET
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0,3
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COMMENT
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These are the numerators of a(n)=(integral_{x=0 to 1/3} (1-.5*x)^n dx). E.g. a(3)=671/2592. The denominators are b(n)=3*(n+1)*6^n. E.g. b(3)=2592. the subscripts in both cases are 0. - Al Hakanson (hawkuu(AT)excite.com), Feb 22 2004
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FORMULA
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G.f.: x/((1-5x)(1-6x)).
a(n)=11*a(n-1)-30*a(n-2), n>1 ; a(0)=0, a(1)=1 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jan 01 2009]
E.g.f.: e^(6*x)-e^(5*x). [From Mohammad K. Azarian (azarian(AT)evansville.edu), Jan 14 2009]
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MAPLE
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restart:a:=n->sum(5^(n-j)*binomial(n, j), j=1..n): seq(a(n), n=0..19); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 18 2009]
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PROGRAM
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(Other) sage: [lucas_number1(n, 11, 30) for n in xrange(0, 20)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 27 2009]
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CROSSREFS
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Sequence in context: A088779 A055083 A016160 this_sequence A125374 A126532 A117611
Adjacent sequences: A005059 A005060 A005061 this_sequence A005063 A005064 A005065
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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