OFFSET
1,2
COMMENTS
Sequence extrapolated to n=1 using recurrence. - Andrew Howroyd, May 16 2017
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..200
Eric Weisstein's World of Mathematics, Matching
Eric Weisstein's World of Mathematics, Maximal Independent Edge Set
Eric Weisstein's World of Mathematics, Prism Graph
Index entries for linear recurrences with constant coefficients, signature (1,2, 1,-1,2,1,-1,-1).
FORMULA
From Andrew Howroyd, May 16 2017 (Start)
a(n) = a(n-1)+2*a(n-2)+a(n-3)-a(n-4)+2*a(n-5)+a(n-6)-a(n-7)-a(n-8) for n>8.
G.f.: x*(-8*x^7-7*x^6+6*x^5+10*x^4 -4*x^3+3*x^2+4*x+1)/((x^2-x+1)*(x^3-x-1)*(x^3+2*x^2+x-1)).
(End)
MATHEMATICA
LinearRecurrence[{1, 2, 1, -1, 2, 1, -1, -1}, {1, 5, 10, 17, 51, 98, 211, 457}, 40] (* Vincenzo Librandi, May 17 2017 *)
CoefficientList[Series[(-8 x^7 - 7 x^6 + 6 x^5 + 10 x^4 - 4 x^3 + 3 x^2 + 4 x + 1) / ((x^2 - x + 1) (x^3 - x - 1) (x^3 + 2 x^2 + x - 1)), {x, 0, 33}], x] (* Vincenzo Librandi, May 17 2017 *)
Table[2 Cos[n Pi/3] + RootSum[-1 - 2 # - #^2 + #^3 &, #^n &] +
RootSum[-1 + #^2 + #^3 &, #^n &], {n, 20}] (* Eric W. Weisstein, May 17 2017 *)
PROG
(PARI)
Vec((-8*x^7-7*x^6+6*x^5+10*x^4-4*x^3+3*x^2+4*x+1)/((x^2-x+1)*(x^3-x-1)*(x^3+2*x^2+x-1))+O(x^20)) \\ Andrew Howroyd, May 16 2017
(Magma) I:=[1, 5, 10, 17, 51, 98, 211, 457]; [n le 8 select I[n] else Self(n-1)+2*Self(n-2)+Self(n-3)-Self(n-4)+2*Self(n-5)+Self(n-6)-Self(n-7)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, May 17 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Apr 01 2017
EXTENSIONS
a(1)-a(2) and a(20)-a(32) from Andrew Howroyd, May 16 2017
STATUS
approved