

A164949


Number of different ways to select 4 disjoint subsets from {1..n} with equal element sum.


9



0, 0, 0, 0, 0, 0, 1, 3, 9, 23, 67, 203, 693, 2584, 9929, 37480, 137067, 522854, 2052657, 8199728, 33456333, 137831268, 574295984, 2392149818, 9950364020, 41860671346, 177512155194, 757447761138, 3254519322231, 14049972380612, 60960849334377, 265354255338637
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,8


LINKS

Table of n, a(n) for n=1..32.


EXAMPLE

a(7) = 1, because {1,6}, {2,5}, {3,4}, {7} are disjoint subsets of {1..7} with element sum 7.
a(8) = 3: {1,6}, {2,5}, {3,4}, {7} have element sum 7, {1,7}, {2,6}, {3,5}, {8} have element sum 8, and {1,8}, {2,7}, {3,6}, {4,5} have element sum 9.


MAPLE

b:= proc() option remember; local i, j; `if` (args[1]=0 and args[2]=0 and args[3]=0 and args[4]=0, 1, `if` (add (args[j], j=1..4)> args[5] *(args[5]1)/2, 0, b(args[j]$j=1..4, args[5]1)) +add (`if` (args[j] args[5]<0, 0, b(sort ([seq (args[i] `if` (i=j, args[5], 0), i=1..4)])[], args[5]1)), j=1..4)) end: a:= n> add (b (k$4, n), k=7..floor (n*(n+1)/8)) /24: seq (a(n), n=1..20);


CROSSREFS

Column k=4 of A196231. Cf. A161943, A164934.
Sequence in context: A047085 A018044 A047045 * A146661 A004666 A196488
Adjacent sequences: A164946 A164947 A164948 * A164950 A164951 A164952


KEYWORD

nonn


AUTHOR

Alois P. Heinz, Sep 01 2009


STATUS

approved



