OFFSET
1,1
COMMENTS
Sequence extrapolated to n=1 using recurrence. - Andrew Howroyd, Dec 30 2017
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..200
Eric Weisstein's World of Mathematics, Crossed Prism Graph
Eric Weisstein's World of Mathematics, Matching
Eric Weisstein's World of Mathematics, Maximal Independent Edge Set
Index entries for linear recurrences with constant coefficients, signature (5, -4, 14, 4, 8).
FORMULA
From Andrew Howroyd, Dec 30 2017: (Start)
a(n) = 5*a(n-1) - 4*a(n-2) + 14*a(n-3) + 4*a(n-4) + 8*a(n-5) for n > 5.
G.f.: x*(5 - 8*x + 42*x^2 + 16*x^3 + 40*x^4)/(1 - 5*x + 4*x^2 - 14*x^3 - 4*x^4 - 8*x^5).
(End)
MATHEMATICA
Table[RootSum[-8 - 4 # - 14 #^2 + 4 #^3 - 5 #^4 + #^5 & , #^n &], {n, 20}]
RootSum[-8 - 4 # - 14 #^2 + 4 #^3 - 5 #^4 + #^5 & , #^Range[20] &]
LinearRecurrence[{5, -4, 14, 4, 8}, {5, 17, 107, 553, 2635}, 20]
CoefficientList[Series[(-5 + 8 x - 42 x^2 - 16 x^3 - 40 x^4)/(-1 + 5 x - 4 x^2 + 14 x^3 + 4 x^4 + 8 x^5), {x, 0, 20}], x]
PROG
(PARI) Vec((5 - 8*x + 42*x^2 + 16*x^3 + 40*x^4)/(1 - 5*x + 4*x^2 - 14*x^3 - 4*x^4 - 8*x^5) + O(x^30)) \\ Andrew Howroyd, Dec 30 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Dec 30 2017
STATUS
approved