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%I #38 Mar 09 2024 11:04:46
%S 0,2,2,14,18,94,146,638,1138,4382,8658,30398,64818,212574,479890,
%T 1496062,3525106,10581918,25748306,75139390,187301554,535144670,
%U 1358396434,3820058238,9829858162,27316621854,71015537874,195595836350,512422576178,1401935442782
%N a(n) is the number of n-walks between the vertices 1 and 3 of the Graph on the chalkboard in 'Good Will Hunting', (1997).
%C For a presentation of the Graph, see the first link.
%D Burkard Polster & Marty Ross, Math Goes to the Movies, The Johns Hopkins University Press, Baltimore, 2013, ยง1.7 Mathematics: Graph Theory 1, pp. 9-12.
%H Oliver Knill, Harvard Math, <a href="http://www.math.harvard.edu/archive/21b_fall_03/goodwill/">The Good Will Hunting Problem</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Good_Will_Hunting">Good Will Hunting</a>
%H MMDB-The Mathematical Movie Database, Burkard Polster & Marty Ross, <a href="http://www.qedcat.com/moviemath/GoodWill.htm">Good Will Hunting</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,6,-4).
%F G.f.: 2*x^2/(1 - x - 6*x^2 + 4*x^3).
%e "For example, between the vertices 1 and 3, we can calculate that there are no 1-walks, two 2-walks, two 3-walks and so on. The resulting sequence of numbers begins 0, 2, 2, 14, 18, 94, 146, 638, ..." (p. 11).
%t LinearRecurrence[{1, 6, -4}, {0, 2, 2}, 30] (* Or *)
%t Rest@ CoefficientList[Series[2x^2/(1 - x - 6x^2 + 4x^3), {x, 0, 28}], x]
%o (PARI) Vec(2*x^2/(1 - x - 6*x^2 + 4*x^3)+O(x^99)) \\ _Charles R Greathouse IV_, May 21 2013
%K nonn,easy,walk
%O 1,2
%A Oliver Knill (knill(AT)math.harvard.edu), Burkard Polster (burkard.polster(AT)monash.edu), Marty Ross (martinirossi(AT)gmail.com), and _Robert G. Wilson v_, Jan 02 2013
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