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A002985 Number of trees in an n-node wheel.
(Formerly M0783)
1
1, 1, 1, 2, 3, 6, 11, 20, 36, 64, 108, 179, 292, 464, 727, 1124, 1714, 2585, 3866, 5724, 8418, 12290, 17830, 25713, 36898, 52664, 74837, 105873, 149178, 209364, 292793, 407990, 566668, 784521, 1082848, 1490197, 2045093, 2798895, 3820629, 5202085 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

This is the number of nonequivalent spanning trees of the n-wheel graph up to isomorphism of the trees.

REFERENCES

F. Harary, P. E. O'Neil, R. C. Read and A. J. Schwenk, The number of trees in a wheel, in D. J. A. Welsh and D. R. Woodall, editors, Combinatorics. Institute of Mathematics and Its Applications. Southend-on-Sea, England, 1972, pp. 155-163.

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

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..200

Index entries for sequences related to trees

Andrew Howroyd, Derivation of formula

Eric Weisstein's World of Mathematics, Wheel Graph

FORMULA

a(n) = A003293(n-1) - A008804(n-3). - Andrew Howroyd, Oct 09 2017

EXAMPLE

All trees that span a wheel on 5 nodes are equivalent to one of the following:

      o         o         o

      |         | \     /   \

   o--o--o   o--o  o   o--o  o

      |         |           /

      o         o         o

PROG

(PARI) \\ here b(n) is A003293 and d(n) is A008804.

b(n)={polcoeff( prod(k=1, n, (1-x^k+x*O(x^n))^-ceil(k/2)), n)}

d(n)={(84+12*(-1)^n+6*I*((-I)^n-I^n)+(85+3*(-1)^n)*n+24*n^2+2*n^3)/96}

a(n)=b(n-1)-d(n-3); \\ Andrew Howroyd, Oct 09 2017

CROSSREFS

Cf. A003293, A004146, A008804.

Sequence in context: A131269 A047081 A090167 * A239342 A093608 A079976

Adjacent sequences:  A002982 A002983 A002984 * A002986 A002987 A002988

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Terms a(32) and beyond from Andrew Howroyd, Oct 09 2017

STATUS

approved

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Last modified November 23 00:33 EST 2017. Contains 295107 sequences.