A261481 Number of set partitions of [n] into exactly five parts such that no part contains two elements with a circular distance less than three.

1, 3, 14, 44, 138, 458, 1397, 4219, 12974, 39270, 118004, 355924, 1071425, 3217011, 9662070, 29016280, 87083486, 261322358, 784185253, 2352907211, 7059288006, 21179391714, 63541238088, 190628647440, 571896993217, 1715715461187, 5147189398142, 15441653075684

Offset

5,2

Links

Alois P. Heinz, Table of n, a(n) for n = 5..1000

Index entries for linear recurrences with constant coefficients, signature (2,1,12,-6,-18,-47,-32,17,36,36).

Formula

G.f.: -(6*x^5+6*x^4+x^3+7*x^2+x+1)*x^5 / ((x-1) *(3*x-1) *(2*x-1) *(x+1) *(x^2+x+1) *(3*x^2+x+1) *(2*x^2+x+1)).

a(n) = 2*a(n-1) + a(n-2) + 12*a(n-3) - 6*a(n-4) - 18*a(n-5) - 47*a(n-6) - 32*a(n-7) + 17*a(n-8) + 36*a(n-9) + 36*a(n-10). - Wesley Ivan Hurt, Apr 16 2023

Example

a(5) = 1: 1|2|3|4|5.
a(6) = 3: 14|2|3|5|6, 1|25|3|4|6, 1|2|36|4|5.
a(7) = 14: 14|25|3|6|7, 14|26|3|5|7, 14|2|36|5|7, 14|2|37|5|6, 15|26|3|4|7, 15|2|36|4|7, 15|2|37|4|6, 15|2|3|47|6, 1|25|36|4|7, 1|25|37|4|6, 1|25|3|47|6, 1|26|37|4|5, 1|26|3|47|5, 1|2|36|47|5.

Crossrefs

Column k=5 of A261477.

Sequence in context: A305009 A115005 A058389 * A059672 A302225 A032316

Adjacent sequences: A261478 A261479 A261480 * A261482 A261483 A261484

Keyword

nonn,easy

Author

Alois P. Heinz, Aug 20 2015

Status

approved