A261482 Number of set partitions of [n] into exactly six parts such that no part contains two elements with a circular distance less than three.

1, 7, 42, 210, 985, 4400, 18944, 80067, 333431, 1372364, 5607350, 22788432, 92221903, 372094575, 1498066156, 6021295070, 24172138331, 96949953648, 388584438750, 1556689868075, 6233817797545, 24956454853128, 99889360100264, 399748052249200, 1599564125648941

Offset

6,2

Links

Alois P. Heinz, Table of n, a(n) for n = 6..1000

Index entries for linear recurrences with constant coefficients, signature (5,-5,25,-74,-16,-185,205,401,737,440,-380,-576,-576).

Formula

G.f.: (24*x^7+24*x^6+9*x^5+44*x^4+10*x^3+12*x^2+2*x+1) *x^6 / ((x-1) *(3*x-1) *(2*x-1) *(4*x-1) *(x+1) *(x^2+x+1) *(3*x^2+x+1) *(2*x^2+x+1) *(4*x^2+x+1)).

Example

a(6) = 1: 1|2|3|4|5|6.
a(7) = 7: 14|2|3|5|6|7, 15|2|3|4|6|7, 1|25|3|4|6|7, 1|26|3|4|5|7, 1|2|36|4|5|7, 1|2|37|4|5|6, 1|2|3|47|5|6.
a(8) = 42: 14|25|3|6|7|8, 14|26|3|5|7|8, 14|2|36|5|7|8, 14|27|3|5|6|8, 14|2|37|5|6|8, 14|2|38|5|6|7, 14|2|3|58|6|7, 15|26|3|4|7|8, 15|2|36|4|7|8, 15|27|3|4|6|8, 15|2|37|4|6|8, 15|2|3|47|6|8, 15|2|38|4|6|7, 15|2|3|48|6|7, 16|25|3|4|7|8, 1|25|36|4|7|8, 1|25|37|4|6|8, 1|25|3|47|6|8, 1|25|38|4|6|7, 1|25|3|48|6|7, 16|27|3|4|5|8, 16|2|37|4|5|8, 16|2|3|47|5|8, 16|2|38|4|5|7, 16|2|3|48|5|7, 16|2|3|4|58|7, 1|26|37|4|5|8, 1|26|3|47|5|8, 1|26|38|4|5|7, 1|26|3|48|5|7, 1|26|3|4|58|7, 1|27|36|4|5|8, 1|2|36|47|5|8, 1|2|36|48|5|7, 1|2|36|4|58|7, 1|27|38|4|5|6, 1|27|3|48|5|6, 1|27|3|4|58|6, 1|2|37|48|5|6, 1|2|37|4|58|6, 1|2|38|47|5|6, 1|2|3|47|58|6.

Crossrefs

Column k=6 of A261477.

Sequence in context: A092072 A319890 A319871 * A215226 A349427 A200864

Adjacent sequences: A261479 A261480 A261481 * A261483 A261484 A261485

Keyword

nonn,easy

Author

Alois P. Heinz, Aug 20 2015

Status

approved