A178185 -id:A178185 - cp's OEIS frontend

A320333 a(n) is the number of pairings of the first 2k positive integers into k pairs (xi, yi) such that the k numbers (xi + yi) mod k are all different where k = 2n + 1.

1, 9, 145, 4641, 231417, 16770369, 1671395713

Offset: 0

Altug Alkan, Oct 11 2018

It can be seen as interesting that a(t) = A178185(t+1) for 0 <= t <= 3.

			a(1) = 9 because {(1,4), (2,5), (3,6)}, {(1,5), (2,6), (3,4)}, {(1,6), (2,4), (3,5)}, {(1,3), (2,6), (4,5)}, {(1,5), (2,3), (4,6)}, {(1,6), (2,3), (4,5)}, {(1,3), (2,4), (5,6)}, {(1,2), (3,5), (4,6)}, {(1,2), (3,4), (5,6)} are corresponding sets.

Cf. A060963, A178185, A320129.

A371441 a(n) = a(n-1)*3^n + 1 where a(0)=1.

Original entry on oeis.org

1, 4, 37, 1000, 81001, 19683244, 14349084877, 31381448626000, 205893684435186001, 4052605390737766057684, 239302295717674347940182517, 42391683779498857714559512339000, 22528678819460652442683221796950499001, 35917990801478965784376042224979510418771324

Offset: 0

Alexandre Herrera, Mar 23 2024

Cf. A073587, A178185.

Table[Sum[3^(k*(2*n + 1 - k)/2), {k, 0, n}], {n, 0, 15}] (* Vaclav Kotesovec, Apr 10 2024 *)
Block[{n = 0}, NestList[#*3^++n + 1 &, 1, 15]] (* Paolo Xausa, Apr 19 2024 *)

l = [1]
for i in range(1,14):
    l.append(l[-1]*pow(3,i) + 1)
print(l)

a(n) = Sum_{k=0..n} 3^(k*(2*n + 1 - k)/2). - Vaclav Kotesovec, Apr 10 2024

cp's OEIS Frontend

A320333 a(n) is the number of pairings of the first 2k positive integers into k pairs (xi, yi) such that the k numbers (xi + yi) mod k are all different where k = 2n + 1.

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A371441 a(n) = a(n-1)*3^n + 1 where a(0)=1.

Views

Author

Keywords

Crossrefs

Programs

Mathematica

Python

Formula

cp's OEIS Frontend

A320333 a(n) is the number of pairings of the first 2*k positive integers into k pairs (xi, yi) such that the k numbers (xi + yi) mod k are all different where k = 2*n + 1.

Views

Author

Keywords

Comments

Examples

Crossrefs

A371441 a(n) = a(n-1)*3^n + 1 where a(0)=1.

Views

Author

Keywords

Crossrefs

Programs

Mathematica

Python

Formula

A320333 a(n) is the number of pairings of the first 2k positive integers into k pairs (xi, yi) such that the k numbers (xi + yi) mod k are all different where k = 2n + 1.