A231074 The number of possible ways to arrange the sums x_i + x_j (1 <= i < j <= n) of the items x_1 < x_2 <...< x_n in nondecreasing order.

1, 1, 1, 1, 2, 12, 244

Offset

0,5

Comments

For n<=5, a(n) = A003121(n), but for n > 5, a(n) < A003121(n).

Every possible ordering of sums provides a way of placing 1,2,...,n(n+1)/2 in a triangular array such that both rows and columns are increasing, but the reverse is generally not true.

Links

Table of n, a(n) for n=0..6.

Vladimir Letsko, Mathematical Marathon, Problem 183 (in Russian)

Example

Let a < b < c < d. There are two possible ways to arrange the sums in nondecreasing order:
1) a+b <= a+c <= a+d <= b+c <= b+d <= c+d, (for instance, a = 1, b = 3, c = 4, d = 5);
2) a+b <= a+c <= b+c <= a+d <= b+d <= c+d, (for instance, a = 1, b = 2, c = 3, d = 5).
Hence a(4) = 2.

Crossrefs

Cf. A231085, A003121, A237749.

Sequence in context: A325501 A007986 A013503 * A132481 A369680 A217652

Adjacent sequences: A231071 A231072 A231073 * A231075 A231076 A231077

Keyword

nonn,more

Author

Vladimir Letsko, Nov 03 2013

Extensions

Term a(0)=1 prepended by Max Alekseyev, Feb 23 2014

Status

approved