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Search: id:A023000
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| 0, 1, 8, 57, 400, 2801, 19608, 137257, 960800, 6725601, 47079208, 329554457, 2306881200, 16148168401, 113037178808, 791260251657, 5538821761600, 38771752331201, 271402266318408, 1899815864228857, 13298711049602000
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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7^(floor(7^n/6)) is the highest power of 7 dividing (7^n)! - Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 04 2002
Except for the first term, a(n)=7*a(n-1)+1 (with a(1)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Oct 29 2009]
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
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((4+sqrt9)^n-(4-sqrt9)^n/6. Offset 1. a(3)=57 [From Al Hakanson (hawkuu(AT)gmail.com), Jan 07 2009]
a(n)=8*a(n-1)-7*a(n-2). G.f.: x/((1-x)(1-7x)). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 21 2009]
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MAPLE
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a:=n->sum(7^(n-j), j=1..n): seq(a(n), n=0..20); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 04 2007
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MATHEMATICA
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lst={}; Do[p=(7^n-1)/6; AppendTo[lst, p], {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 29 2008]
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PROGRAM
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(Other) sage: [lucas_number1(n, 8, 7) for n in xrange(0, 21)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 23 2009]
(Other) sage: [gaussian_binomial(n, 1, 7) for n in xrange(0, 21)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 28 2009]
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CROSSREFS
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Sequence in context: A079926 A108666 A164031 this_sequence A097114 A022038 A015453
Adjacent sequences: A022997 A022998 A022999 this_sequence A023001 A023002 A023003
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KEYWORD
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easy,nonn
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AUTHOR
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David W. Wilson (davidwwilson(AT)comcast.net)
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