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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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9
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0, 1, 8, 73, 656, 5905, 53144, 478297, 4304672, 38742049, 348678440, 3138105961, 28242953648, 254186582833, 2287679245496, 20589113209465, 185302018885184, 1667718169966657, 15009463529699912, 135085171767299209, 1215766545905692880, 10941898913151235921
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| 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
General form: k=9^n-k. Also: A001045, A078008, A097073, A115341, A015518, A054878, A015521, A109499, A015531, A109500, A109501, A015552, A093134, A015565 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 11 2008]
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index to sequences with linear recurrences with constant coefficients, signature (8,9).
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FORMULA
| G.f.: x/((1+x)*(1-9*x)); E.g.f.: exp(4*x)*sinh(5*x)/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
a(n)=round(9^n/10). [From Mircea Merca, Dec 28 2010]
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MAPLE
| seq(round(9^n/10), n=0..25) [From Mircea Merca, Dec 28 2010]
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MATHEMATICA
| k=0; lst={k}; Do[k=9^n-k; AppendTo[lst, k], {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 11 2008]
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PROG
| (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
(Sage) [lucas_number1(n, 8, -9) for n in xrange(0, 19)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 25 2009]
(MAGMA) [Round(9^n/10): n in [0..30]]; // Vincenzo Librandi, Jun 24 2011
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CROSSREFS
| Cf. A001045, A078008, A097073, A115341, A015518, A054878, A015521, A109499, A015531, A109500, A109501, A015552, A093134, A015565 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 11 2008]
Sequence in context: A096873 A153482 A014991 * A082764 A024104 A152429
Adjacent sequences: A015574 A015575 A015576 * A015578 A015579 A015580
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KEYWORD
| nonn,easy
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AUTHOR
| Olivier Gerard (olivier.gerard(AT)gmail.com)
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EXTENSIONS
| Extended by T. D. Noe (noe(AT)sspectra.com), May 23 2011
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