A015592 - OEIS

%I #28 Aug 17 2024 20:40:28

%S 0,1,10,111,1220,13421,147630,1623931,17863240,196495641,2161452050,

%T 23775972551,261535698060,2876892678661,31645819465270,

%U 348104014117971,3829144155297680,42120585708274481,463326442791019290,5096590870701212191,56062499577713334100

%N a(n) = 10*a(n-1) + 11*a(n-2).

%C Number of walks of length n between any two distinct nodes of the complete graph K_12. Example: a(2)=10 because the walks of length 2 between the nodes A and B of the complete graph ABCDEFGHIJKL are ACB, ADB, AEB, AFB, AGB, AHB, AIB, AJB, AKB and ALB. - _Emeric Deutsch_, Apr 01 2004

%C General form: k=11^n-k. Also: A001045, A078008, A097073, A115341, A015518, A054878, A015521, A109499, A015531, A109500, A109501, A015552, A093134, A015565, A015577, A015585. - _Vladimir Joseph Stephan Orlovsky_, Dec 11 2008

%H Vincenzo Librandi, <a href="/A015592/b015592.txt">Table of n, a(n) for n = 0..900</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,11).

%F a(n) = 11^(n-1) - a(n-1). G.f.: x/(1 - 10x - 11x^2). - _Emeric Deutsch_, Apr 01 2004

%F From _Elmo R. Oliveira_, Aug 17 2024: (Start)

%F E.g.f.: exp(5*x)*sinh(6*x)/6.

%F a(n) = (11^n - (-1)^n)/12. (End)

%t k=0;lst={k};Do[k=11^n-k;AppendTo[lst, k], {n, 0, 5!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Dec 11 2008 *)

%o (Sage) [lucas_number1(n,10,-11) for n in range(0, 18)] # _Zerinvary Lajos_, Apr 26 2009

%o (Magma) [-(1/12)*(-1)^n+(1/12)*11^n: n in [0..20]]; // _Vincenzo Librandi_, Oct 11 2011

%Y Cf. A001045, A078008, A097073, A115341, A015518, A054878, A015521, A109499, A015531, A109500, A109501, A015552, A093134, A015565, A015577, A015585. - _Vladimir Joseph Stephan Orlovsky_, Dec 11 2008

%K nonn,easy

%O 0,3

%A _Olivier Gérard_