OFFSET
4,1
COMMENTS
The square knight graph is connected for n >= 4.
LINKS
Colin Barker, Table of n, a(n) for n = 4..1000
Eric Weisstein's World of Mathematics, Knight Graph
Eric Weisstein's World of Mathematics, Wiener Index
Index entries for linear recurrences with constant coefficients, signature (2,1,-3,0,-1,2,2,-1,0,-3,1,2,-1).
FORMULA
a(n) = 2*a(n-1) + a(n-2) - 3*a(n-3) - a(n-5) + 2*a(n-6) + 2*a(n-7) - a(n-8) - 3*a(n-10) + a(n-11) + 2*a(n-12) - a(n-13) for n > 17.
G.f.: 4*x^4*(72 + 33*x - 31*x^2 + 35*x^3 + 15*x^4 + 68*x^5 + 39*x^6 - 28*x^7 - 14*x^8 - 60*x^9 + 37*x^10 + 36*x^11 - 26*x^12 + 2*x^13) / ((1 - x)^6*(1 + x)^3*(1 + x^2)*(1 + x + x^2)). - Colin Barker, Sep 18 2017
MATHEMATICA
Join[{288}, LinearRecurrence[{2, 1, -3, 0, -1, 2, 2, -1, 0, -3, 1, 2, -1}, {708, 1580, 3144, 5804, 9996, 16388, 25660, 38808, 56808, 81048, 112856, 154080, 206448}, 20]]
PROG
(PARI) Vec(4*x^4*(72 + 33*x - 31*x^2 + 35*x^3 + 15*x^4 + 68*x^5 + 39*x^6 - 28*x^7 - 14*x^8 - 60*x^9 + 37*x^10 + 36*x^11 - 26*x^12 + 2*x^13) / ((1 - x)^6*(1 + x)^3*(1 + x^2)*(1 + x + x^2)) + O(x^50)) \\ Colin Barker, Sep 18 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Sep 08 2017
STATUS
approved