A261483 Number of set partitions of [n] into exactly seven parts such that no part contains two elements with a circular distance less than three.

1, 12, 102, 720, 4587, 27326, 155571, 858023, 4623388, 24488768, 128053146, 663054996, 3407483161, 17409523182, 88545747922, 448749879028, 2267921345677, 11436557773522, 57571373075875, 289413549581585, 1453301573317896, 7291464343122268, 36557211011698580

Offset

7,2

Links

Alois P. Heinz, Table of n, a(n) for n = 7..1000

Index entries for linear recurrences with constant coefficients, signature (9,-25,70,-299,405,-746,2795,-19,3758,-7633,-12165,-17481,-9272,11804,14400,14400).

Formula

G.f.: -(120*x^9 +120*x^8 +71*x^7 +296*x^6 +86*x^5 +116*x^4 +32*x^3 +19*x^2 +3*x+1) *x^7 / ((x-1) *(5*x-1) *(3*x-1) *(2*x-1) *(4*x-1) *(x+1) *(x^2+x+1) *(5*x^2+x+1) *(3*x^2+x+1) *(4*x^2+x+1) *(2*x^2+x+1)).

Example

a(7) = 1: 1|2|3|4|5|6|7.
a(8) = 12: 14|2|3|5|6|7|8, 15|2|3|4|6|7|8, 1|25|3|4|6|7|8, 16|2|3|4|5|7|8, 1|26|3|4|5|7|8, 1|2|36|4|5|7|8, 1|27|3|4|5|6|8, 1|2|37|4|5|6|8, 1|2|3|47|5|6|8, 1|2|38|4|5|6|7, 1|2|3|48|5|6|7, 1|2|3|4|58|6|7.

Crossrefs

Column k=7 of A261477.

Sequence in context: A304504 A344279 A022736 * A082151 A125375 A217057

Adjacent sequences: A261480 A261481 A261482 * A261484 A261485 A261486

Keyword

nonn,easy

Author

Alois P. Heinz, Aug 20 2015

Status

approved