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A015585
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a(n) = 9*a(n-1) + 10*a(n-2).
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9
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0, 1, 9, 91, 909, 9091, 90909, 909091, 9090909, 90909091, 909090909, 9090909091, 90909090909, 909090909091, 9090909090909, 90909090909091, 909090909090909, 9090909090909091, 90909090909090909, 909090909090909091, 9090909090909090909, 90909090909090909091
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OFFSET
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0,3
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COMMENTS
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Number of walks of length n between any two distinct nodes of the complete graph K_11. Example: a(2)=9 because the walks of length 2 between the nodes A and B of the complete graph ABCDEFGHIJK are: ACB, ADB, AEB, AFB, AGB, AHB, AIB, AJB and AKB. - Emeric Deutsch, Apr 01 2004
Beginning with n=1 and a(1)=1, these are the positive integers whose balanced base-10 representations (A097150) are the first n digits of 1,-1,1,-1,.... Also, a(n) = (-1)^(n-1)*A014992(n) = |A014992(n)| for n >= 1. - Rick L. Shepherd, Jul 30 2004
General form: k=10^n-k. Also: A001045, A078008, A097073, A115341, A015518, A054878, A015521, A109499, A015531, A109500, A109501, A015552, A093134, A015565, A015577. - Vladimir Joseph Stephan Orlovsky, Dec 11 2008
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LINKS
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FORMULA
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a(n) = 9*a(n-1) + 10*a(n-2).
a(n) = 10^(n-1) - a(n-1).
G.f.: x/(1 - 9x - 10x^2). (End)
a(n) = round(10^n/11).
a(n) = (10^n - (-1)^n)/11.
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MATHEMATICA
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LinearRecurrence[{9, 10}, {0, 1}, 30] (* Harvey P. Dale, Aug 08 2014 *)
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PROG
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(Sage) [lucas_number1(n, 9, -10) for n in range(0, 19)] # Zerinvary Lajos, Apr 26 2009
(Sage) [abs(gaussian_binomial(n, 1, -10)) for n in range(0, 19)] # Zerinvary Lajos, May 28 2009
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CROSSREFS
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Cf. A001045, A078008, A097073, A115341, A015518, A054878, A015521, A109499, A015531, A109500, A109501, A015552, A093134, A015565, A015577. - Vladimir Joseph Stephan Orlovsky, Dec 11 2008
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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