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Search: id:A015585
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| A015585 |
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Linear 2nd order recurrence. |
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+0
5
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| 0, 1, 9, 91, 909, 9091, 90909, 909091, 9090909, 90909091, 909090909, 9090909091, 90909090909, 909090909091, 9090909090909, 90909090909091, 909090909090909, 9090909090909091, 90909090909090909
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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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 (deutsch(AT)duke.poly.edu), 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 (rshepherd2(AT)hotmail.com), Jul 30 2004
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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). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 01 2004
a(n) = round[10^n/11] = (10^n-(-1)^n)/11 = A098611(n)/11 = 9*A094028(n+1)/A098610(n). - Henry Bottomley (se16(AT)btinternet.com), Sep 17 2004
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CROSSREFS
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Cf. A014992 (q-integers for q=-10), A097150.
Adjacent sequences: A015582 A015583 A015584 this_sequence A015586 A015587 A015588
Sequence in context: A077334 A020243 A014992 this_sequence A109108 A123792 A022520
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KEYWORD
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nonn,easy
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AUTHOR
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Olivier Gerard (olivier.gerard(AT)gmail.com)
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