A015577 a(n+1) = 8*a(n) + 9*a(n-1), a(0) = 0, a(1) = 1.

0, 1, 8, 73, 656, 5905, 53144, 478297, 4304672, 38742049, 348678440, 3138105961, 28242953648, 254186582833, 2287679245496, 20589113209465, 185302018885184, 1667718169966657, 15009463529699912, 135085171767299209, 1215766545905692880, 10941898913151235921

Offset

0,3

Comments

Binomial transform is A011557, with a leading zero. - Paul Barry, 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, Apr 01 2004

The ratio a(n+1)/a(n) converges to 9 as n approaches infinity. - Felix P. Muga II, Mar 09 2014

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Jean-Paul Allouche, Jeffrey Shallit, Zhixiong Wen, Wen Wu, Jiemeng Zhang, Sum-free sets generated by the period-k-folding sequences and some Sturmian sequences, arXiv:1911.01687 [math.CO], 2019.

Martin Burtscher, Igor Szczyrba, Rafał Szczyrba, Analytic Representations of the n-anacci Constants and Generalizations Thereof, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5.

Index entries for linear recurrences with constant coefficients, signature (8,9).

Formula

From Paul Barry, Jul 09 2003: (Start)

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. (End)

a(n) = 9^(n-1)-a(n-1). - Emeric Deutsch, Apr 01 2004

a(n) = round(9^n/10). - Mircea Merca, Dec 28 2010

Maple

seq(round(9^n/10), n=0..25); # Mircea Merca, Dec 28 2010

Mathematica

k=0; lst={k}; Do[k=9^n-k; AppendTo[lst, k], {n, 0, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 11 2008 *)
Table[(9^n - (-1)^n)/10, {n, 0, 30}] (* or *) LinearRecurrence[{8, 9}, {0, 1}, 30] (* G. C. Greubel, Jan 06 2018 *)

Prog

(PARI) A015577_vec(N=20)=Vec(O(x^N)+1/(1-8*x-9*x^2), -N-1) \\ M. F. Hasler, Jun 14 2008, edited Oct 25 2019
(PARI) for(n=0, 30, print1((9^n - (-1)^n)/10, ", ")) \\ G. C. Greubel, Jan 06 2018
(PARI) apply( {A015577(n)=9^n\/10}, [0..25]) \\ M. F. Hasler, Oct 25 2019
(Sage) [lucas_number1(n, 8, -9) for n in range(0, 19)] # Zerinvary Lajos, Apr 25 2009
(Magma) [Round(9^n/10): n in [0..30]]; // Vincenzo Librandi, Jun 24 2011
(Maxima)
a[0]:0$
a[n]:=9^(n-1)-a[n-1]$
A015577(n):=a[n]$
makelist(A015577(n), n, 0, 30); /* Martin Ettl, Nov 05 2012 */

Crossrefs

Cf. A001045, A078008, A097073, A115341, A015518, A054878, A015521, A109499, A015531, A109500, A109501, A015552, A093134, A015565. - Vladimir Joseph Stephan Orlovsky, Dec 11 2008

Sequence in context: A241630 A153482 A014991 * A293151 A082764 A254150

Adjacent sequences: A015574 A015575 A015576 * A015578 A015579 A015580

Keyword

nonn,easy

Author

Olivier Gérard

Extensions

Extended by T. D. Noe, May 23 2011

Status

approved