A377464 Number of connected pairs of subsets of [n] with each being a different size.

0, 0, 2, 12, 62, 290, 1292, 5579, 23606, 98490, 406862, 1668689, 6807704, 27663441, 112076057, 453031502, 1828018406, 7366128866, 29650536878, 119249689265, 479277846962, 1925216817095, 7729973578307, 31025341749680, 124486445913728, 499362094315865

Offset

0,3

Comments

Empirically, a(A075930(n)) == 1 (mod 2).

Links

Table of n, a(n) for n=0..25.

Formula

a(n) = Sum_{i=0..n-2} binomial(n,i) * Sum_{j=i+1..n-1} (binomial(n,j) - binomial(i,n-j)).

Example

a(3) = 12 counts the pairs: {{1,2},{1}}, {{1,2},{2}}, {{1,3},{1}}, {{1,3},{3}}, {{2,3},{2}}, {{2,3},{3}}, {{1,2,3},{1,2}}, {{1,2,3},{1,3}}, {{1,2,3},{2,3}}, {{1,2,3},{1}}, {{1,2,3},{2}}, {{1,2,3},{3}}.

Prog

(PARI)
A377464(n) = {sum(i=0, n-2, binomial(n, i)*sum(j=i+1, n-1, binomial(n, j)-binomial(i, n-j)))}

Crossrefs

Cf. A001187, A075930, A323818, A326749.

Sequence in context: A245091 A037562 A321277 * A187001 A121177 A125831

Adjacent sequences: A377461 A377462 A377463 * A377465 A377466 A377467

Keyword

nonn,easy

Author

John Tyler Rascoe, Oct 29 2024

Status

approved