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A016123
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(11^(n+1) - 1)/10.
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15
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1, 12, 133, 1464, 16105, 177156, 1948717, 21435888, 235794769, 2593742460, 28531167061, 313842837672, 3452271214393, 37974983358324, 417724816941565, 4594972986357216, 50544702849929377, 555991731349223148
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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
Let A be the Hessenberg matrix of order n, defined by: A[1,j]=1, A[i,i]:=11, (i>1), A[i,i-1]=-1, and A[i,j]=0 otherwise. Then, for n>=1, a(n-1)=det(A). [From Milan R. Janjic (agnus(AT)blic.net), Feb 21 2010]
Let A be the Hessenberg matrix of the order n, defined by: A[1,j]=1, A[i,i]:=12, (i>1), A[i,i-1]=-1, and A[i,j]=0 otherwise. Then, for n>=2, a(n-1)=(-1)^n*charpoly(A,1). [From Milan R. Janjic (agnus(AT)blic.net), Feb 21 2010]
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LINKS
| Eric Weisstein's World of Mathematics, Repunit
Index to sequences with linear recurrences with constant coefficients, signature (12,-11).
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FORMULA
| 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.
a(0)=1, a(n)=11*a(n-1)+1. [From Vincenzo Librandi, Feb 05 2011]
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MAPLE
| 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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MATHEMATICA
| Join[{a=1, b=12}, Table[c=12*b-11*a; a=b; b=c, {n, 60}]] (*From Vladimir Joseph Stephan Orlovsky, Jan 21 2011*)
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PROG
| (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
| Cf. A004191.
Sequence in context: A170693 A120673 A120674 * A015457 A015469 A144785
Adjacent sequences: A016120 A016121 A016122 * A016124 A016125 A016126
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Title edited by Daniel Forgues (kephalopod(AT)gmail.com), Jul 08 2011
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