A187734 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).
0, 2, 2, 14, 18, 94, 146, 638, 1138, 4382, 8658, 30398, 64818, 212574, 479890, 1496062, 3525106, 10581918, 25748306, 75139390, 187301554, 535144670, 1358396434, 3820058238, 9829858162, 27316621854, 71015537874, 195595836350, 512422576178, 1401935442782
Offset: 1
Examples
"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).
References
- 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.
Links
- Oliver Knill, Harvard Math, The Good Will Hunting Problem
- Wikipedia, Good Will Hunting
- MMDB-The Mathematical Movie Database, Burkard Polster & Marty Ross, Good Will Hunting
- Index entries for linear recurrences with constant coefficients, signature (1,6,-4).
Programs
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Mathematica
LinearRecurrence[{1, 6, -4}, {0, 2, 2}, 30] (* Or *) Rest@ CoefficientList[Series[2x^2/(1 - x - 6x^2 + 4x^3), {x, 0, 28}], x] -
PARI
Vec(2*x^2/(1 - x - 6*x^2 + 4*x^3)+O(x^99)) \\ Charles R Greathouse IV, May 21 2013
Formula
G.f.: 2*x^2/(1 - x - 6*x^2 + 4*x^3).
Comments