

A002985


Number of trees in an nnode 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
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OFFSET

1,4


COMMENTS

This is the number of nonequivalent spanning trees of the nwheel 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. SouthendonSea, England, 1972, pp. 155163.
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(n1)  A008804(n3).  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
  \ / \
ooo oo o oo o
  /
o o o


PROG

(PARI) \\ here b(n) is A003293 and d(n) is A008804.
b(n)={polcoeff( prod(k=1, n, (1x^k+x*O(x^n))^ceil(k/2)), n)}
d(n)={(84+12*(1)^n+6*I*((I)^nI^n)+(85+3*(1)^n)*n+24*n^2+2*n^3)/96}
a(n)=b(n1)d(n3); \\ 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



