OFFSET
0,3
COMMENTS
Number of walks of length n between any two distinct nodes of the complete graph K_13. Example: a(2)=11 because the walks of length 2 between the nodes A and B of the complete graph ABCDEFGHIJKLM are ACB, ADB, AEB, AFB, AGB, AHB, AIB, AJB, AKB, ALB and AMB. - Emeric Deutsch, Apr 01 2004
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..900
Index entries for linear recurrences with constant coefficients, signature (11,12).
FORMULA
From Emeric Deutsch, Apr 01 2004: (Start)
a(n) = 12^(n-1) - a(n-1).
G.f.: x/(1 - 11*x - 12*x^2). (End)
E.g.f.: exp(-x)*(exp(13*x) - 1)/13. - Stefano Spezia, Mar 11 2020
MATHEMATICA
CoefficientList[Series[x/(1-11*x-12*x^2), {x, 0, 50}], x] (* or *) LinearRecurrence[{11, 12}, {0, 1}, 30] (* G. C. Greubel, Dec 30 2017 *)
PROG
(Sage) [lucas_number1(n, 11, -12) for n in range(0, 18)] # Zerinvary Lajos, Apr 27 2009
(Sage) [abs(gaussian_binomial(n, 1, -12)) for n in range(0, 18)] # Zerinvary Lajos, May 28 2009
(Magma) [(1/13)*(12^n-(-1)^n): n in [0..20]]; // Vincenzo Librandi, Oct 11 2011
(PARI) x='x+O('x^30); concat([0], Vec(x/(1-11*x-12*x^2))) \\ G. C. Greubel, Dec 30 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved