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Search: id:A015577
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| A015577 |
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a(n+1) = 8 a(n) + 9 a(n-1), a(0) = 0, a(1) = 1. |
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+0
3
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| 0, 1, 8, 73, 656, 5905, 53144, 478297, 4304672, 38742049, 348678440, 3138105961, 28242953648, 254186582833, 2287679245496, 20589113209465, 185302018885184, 1667718169966657, 15009463529699912
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Binomial transform is A011557, with a leading zero. - Paul Barry (pbarry(AT)wit.ie), Jul 09 2003
Number of walks of length n between any two distinct nodes of the complete graph K_10. Example: a(2)=8 because the walks of length 2 between the nodes A and B of the complete graph ABCDEFGHIJ are: ACB, ADB, AEB, AFB, AGB, AHB, AIB, and AJB. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 01 2004
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FORMULA
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G.f.: x/((1+x)(1-9x)); E.g.f.: exp(4x)sinh(5x)/5; a(n)=(9^n-(-1)^n)/10. - Paul Barry (pbarry(AT)wit.ie), Jul 09 2003
a(n)=9^(n-1)-a(n-1). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 01 2004
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PROGRAM
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(PARI) A015577(n)=polcoeff(O(x^n)+1/(1-8*x-9*x^2), n-1) \\ - M. F. Hasler (www.univ-ag.fr/~mhasler), Jun 14 2008
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CROSSREFS
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Sequence in context: A058068 A096873 A014991 this_sequence A082764 A024104 A137140
Adjacent sequences: A015574 A015575 A015576 this_sequence A015578 A015579 A015580
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KEYWORD
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nonn,easy
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AUTHOR
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Olivier Gerard (ogerard(AT)ext.jussieu.fr)
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