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Search: id:A016123
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| A016123 |
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Expansion of 1/((1-x)(1-11x)). |
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+0
16
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| 1, 12, 133, 1464, 16105, 177156, 1948717, 21435888, 235794769, 2593742460, 28531167061, 313842837672, 3452271214393, 37974983358324, 417724816941565, 4594972986357216, 50544702849929377, 555991731349223148
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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11^a(n) is highest power of 11 dividing (11^(n+1))!.
Partial sums of powers of 11 (A001020).
a(n)=[(11^n)-1]/10 - Ctibor O. Zizka (ctibor.zizka(AT)seznam.cz), Feb 18 2008
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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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a(n)= sum(11^k, k=0..n) = (11^(n+1)-1)/10.
G.f.: (1/(1-11*x)-1/(1-x))/(10*x)=1/((1-11*x)*(1-x)).
For analogues with primes 2, 3, 5, 7, 13 and 17 see: A000225, A003462, A003463, A023000, A091030 and A091045, respectively.
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MAPLE
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a:=n->sum(11^(n-j), j=1..n): seq(a(n), n=1..18); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 04 2007
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PROGRAM
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(Other) sage: [lucas_number1(n, 12, 11) for n in xrange(1, 19)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 27 2009]
(Other) sage: [gaussian_binomial(n, 1, 11) for n in xrange(1, 19)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 28 2009]
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CROSSREFS
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Sequence in context: A003954 A120673 A120674 this_sequence A015457 A015469 A144785
Adjacent sequences: A016120 A016121 A016122 this_sequence A016124 A016125 A016126
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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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