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A015592
a(n) = 10*a(n-1) + 11*a(n-2).
4
0, 1, 10, 111, 1220, 13421, 147630, 1623931, 17863240, 196495641, 2161452050, 23775972551, 261535698060, 2876892678661, 31645819465270, 348104014117971, 3829144155297680, 42120585708274481, 463326442791019290, 5096590870701212191, 56062499577713334100
OFFSET
0,3
COMMENTS
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
FORMULA
a(n) = 11^(n-1) - a(n-1). G.f.: x/(1 - 10x - 11x^2). - Emeric Deutsch, Apr 01 2004
From Elmo R. Oliveira, Aug 17 2024: (Start)
E.g.f.: exp(5*x)*sinh(6*x)/6.
a(n) = (11^n - (-1)^n)/12. (End)
MATHEMATICA
k=0; lst={k}; Do[k=11^n-k; AppendTo[lst, k], {n, 0, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 11 2008 *)
PROG
(Sage) [lucas_number1(n, 10, -11) for n in range(0, 18)] # Zerinvary Lajos, Apr 26 2009
(Magma) [-(1/12)*(-1)^n+(1/12)*11^n: n in [0..20]]; // Vincenzo Librandi, Oct 11 2011
KEYWORD
nonn,easy
STATUS
approved