OFFSET
1,1
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..500
Eric Weisstein's World of Mathematics, Cameron Graph.
Eric Weisstein's World of Mathematics, Maximal Independent Vertex Set.
Index entries for linear recurrences with constant coefficients, signature (8,-10,22,-4,7,7,-8,0,1).
FORMULA
G.f.: x*(14 - 21*x + 60*x^2 - 36*x^3 + 30*x^4 + 20*x^5 - 38*x^6 - 4*x^7 + 6*x^8 + x^9)/(1 - 8*x + 10*x^2 - 22*x^3 + 4*x^4 - 7*x^5 - 7*x^6 + 8*x^7 - x^9). - Andrew Howroyd, Sep 02 2025
a(n) = 8*a(n-1)-10*a(n-2)+22*a(n-3)-4*a(n-4)+7*a(n-5)+7*a(n-6)-8*a(n-7)+a(n-9). - Eric W. Weisstein, Sep 02 2025
MATHEMATICA
LinearRecurrence[{8, -10, 22, -4, 7, 7, -8, 0, 1}, {14, 91, 648, 4546, 31864, 223462, 1567173, 10990645, 77077774}, 20] (* Eric W. Weisstein, Sep 02 2025 *)
CoefficientList[Series[(14 - 21 x + 60 x^2 - 36 x^3 + 30 x^4 + 20 x^5 - 38 x^6 - 4 x^7 + 6 x^8 + x^9)/(1 - 8 x + 10 x^2 - 22 x^3 + 4 x^4 - 7 x^5 - 7 x^6 + 8 x^7 - x^9), {x, 0, 20}], x] (* Eric W. Weisstein, Sep 02 2025 *)
Table[RootSum[-1 + 8 #^2 - 7 #^3 - 7 #^4 + 4 #^5 - 22 #^6 + 10 #^7 - 8 #^8 + #^9 &, 164056579589319905 #^n - 76501716644751889 #^(n + 1) - 399869111380576961 #^(n + 2) - 56645343163352924 #^(n + 3) - 493374926421685699 #^(n + 4) - 102362274805533251 #^(n + 5) - 56060500104576775 #^(n + 6) - 86897335390154253 #^(n + 7) + 14038193126372637 #^(n + 8) &]/89017025645800708, {n, 20}] (* Eric W. Weisstein, Feb 15 2026 *)
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
Eric W. Weisstein, Sep 02 2025
EXTENSIONS
a(9) onwards from Andrew Howroyd, Sep 02 2025
STATUS
approved