This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A176042 For odd n, this is the number of partitions of n*(n-1)/2 with all part sizes between 3 and n, inclusive. For even n, this is the number of partitions of n*(n-2)/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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,3 COMMENTS Number of different decompositions of complete graphs on n vertices into cycles (for odd n) or into cycles and a 1-factor (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*(n-1)/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*(n-2)/2 of which only the final partition is counted. For n=5 we have n*(n-1)/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(1-x^i, i = 3 .. n)), x, (1/2)*n*(n-1)+1), x, (1/2)*n*(n-1)) elif n::even then coeff(series(1/(product(1-x^i, i = 3 .. n)), x, (1/2)*n*(n-2)+1), x, (1/2)*n*(n-2)) 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, i-1)+b(n-i, min(n-i, i))))     end: a:= n-> `if`(n::odd, b(n*(n-1)/2, n), b(n*(n-2)/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. Adams-Watters, Nov 17 2011 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 11 18:49 EST 2019. Contains 329925 sequences. (Running on oeis4.)