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A005822 Number of spanning trees in third power of cycle.
(Formerly M1243)
1
1, 1, 2, 4, 11, 16, 49, 72, 214, 319, 947, 1408, 4187, 6223, 18502, 27504, 81769, 121552, 361379, 537196, 1597106, 2374129, 7058377, 10492416, 31194361, 46371025, 137862866, 204935836, 609282227, 905709904, 2692710841, 4002767136, 11900382694, 17690150767 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

G. Baron et al., The number of spanning trees in the square of a cycle, Fib. Quart., 23 (1985), 258-264.

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.

Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992.

Index entries for sequences related to trees

Index entries for linear recurrences with constant coefficients, signature (0,4,0,1,0,4,0,-1).

FORMULA

G.f.: x*(1-x^2)*(x^4+x^3-x^2+x+1) / (x^8-4*x^6-x^4-4*x^2+1).

MAPLE

A005822:=-(z-1)*(1+z)*(z**4+z**3-z**2+z+1)/(-4*z**6-z**4-4*z**2+1+z**8); # [Conjectured (correctly) by Simon Plouffe in his 1992 dissertation.]

PROG

(PARI) Vec(-x*(x-1)*(x+1)*(x^4+x^3-x^2+x+1)/(x^8-4*x^6-x^4-4*x^2+1) + O(x^50)) \\ Colin Barker, Jul 09 2015

CROSSREFS

Sequence in context: A278346 A277867 A278595 * A286293 A167801 A216554

Adjacent sequences:  A005819 A005820 A005821 * A005823 A005824 A005825

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

G.f. adapted to the offset from Colin Barker, Jul 09 2015

STATUS

approved

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Last modified August 21 07:08 EDT 2017. Contains 290862 sequences.