0,3

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]

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

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]

(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

(Other) sage: [lucas_number1(n, 8, -9) for n in xrange(0, 19)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 25 2009]

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 this_sequence A082764 A024104 A152429

Adjacent sequences: A015574 A015575 A015576 this_sequence A015578 A015579 A015580

nonn,easy

Olivier Gerard (olivier.gerard(AT)gmail.com)