

A176042


For odd n, this is the number of partitions of n*(n1)/2 with all part sizes between 3 and n, inclusive. For even n, this is the number of partitions of n*(n2)/2 with all part sizes between 3 and n, inclusive.


1



1, 1, 2, 5, 20, 42, 238, 511, 3311, 7423, 52273, 119739, 894950, 2087761, 16317275, 38616848, 312598141, 748492526, 6233339701, 15070028915, 128475055100, 313137867019, 2722580871465, 6681890398543, 59076953846060, 145856049509351, 1308316471338448
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OFFSET

3,3


COMMENTS

Number of different decompositions of complete graphs on n vertices into cycles (for odd n) or into cycles and a 1factor (for n even) according to a conjecture of Brian Alspach's. This is verified for n <= 14.


LINKS

Alois P. Heinz, Table of n, a(n) for n = 3..500
B. Alspach, Research problems, Problem 3, Discrete Math 36 (1981), page 333.


EXAMPLE

For n=3 we have 1+1+1 = 1+2 = 3 = n*(n1)/2 of which only the final partition is counted.
For n=4 we have 1+1+1+1 = 1+1+2 = 2+2 = 1+3 = 4 = n*(n2)/2 of which only the final partition is counted.
For n=5 we have n*(n1)/2 = 10 and only 3+3+4 = 5+5 are counted.


MAPLE

a := proc (n) local i; option remember; if k::odd then coeff(series(1/(product(1x^i, i = 3 .. n)), x, (1/2)*n*(n1)+1), x, (1/2)*n*(n1)) elif n::even then coeff(series(1/(product(1x^i, i = 3 .. n)), x, (1/2)*n*(n2)+1), x, (1/2)*n*(n2)) end if end proc # Christopher Maitland, Jun 17 2010
# second Maple program:
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<3, 0,
b(n, i1)+b(ni, min(ni, i))))
end:
a:= n> `if`(n::odd, b(n*(n1)/2, n), b(n*(n2)/2, n)):
seq(a(n), n=3..35); # Alois P. Heinz, Feb 21 2019


CROSSREFS

Sequence in context: A192164 A244087 A056726 * A185593 A136899 A136882
Adjacent sequences: A176039 A176040 A176041 * A176043 A176044 A176045


KEYWORD

nonn


AUTHOR

Christopher Maitland (c3053540(AT)uon.edu.au), Apr 07 2010


EXTENSIONS

Definition edited by Franklin T. AdamsWatters, Nov 17 2011


STATUS

approved



