|
|
A297476
|
|
Number of maximal matchings in the 2n-crossed prism graph.
|
|
2
|
|
|
5, 17, 107, 553, 2635, 12569, 60611, 292737, 1412171, 6809817, 32841715, 158395537, 763938843, 3684432713, 17769791107, 85702684353, 413339234987, 1993511754617, 9614594040211, 46370641538673, 223642974511931, 1078617383866281, 5202110473022883
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Sequence extrapolated to n=1 using recurrence. - Andrew Howroyd, Dec 30 2017
|
|
LINKS
|
Eric Weisstein's World of Mathematics, Matching
|
|
FORMULA
|
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
|
|
|
STATUS
|
approved
|
|
|
|