A261485 Number of set partitions of [n] into exactly nine parts such that no part contains two elements with a circular distance less than three.

1, 25, 385, 4675, 49192, 470470, 4205630, 35771452, 293015706, 2331292564, 18128195944, 138415310170, 1041422309315, 7742456506169, 57000743099267, 416275237530251, 3019814800297680, 21785468977120420, 156436446465306280, 1118973520631378880

Offset

9,2

Links

Alois P. Heinz, Table of n, a(n) for n = 9..1000

Formula

G.f.: -(5040*x^13 +5040*x^12 +5104*x^11 +18236*x^10 +7064*x^9 +10984*x^8 +4565*x^7 +3333*x^6 +1137*x^5 +527*x^4 +125*x^3 +39*x^2 +5*x+1) *x^9 / ((x-1) *(6*x-1) *(4*x-1) *(3*x-1) *(2*x-1) *(5*x-1) *(7*x-1) *(x+1) *(x^2+x+1) *(5*x^2+x+1) *(3*x^2+x+1) *(4*x^2+x+1) *(7*x^2+x+1) *(2*x^2+x+1) *(6*x^2+x+1)).

Example

a(9) = 1: 1|2|3|4|5|6|7|8|9.
a(10) = 25: 14|2|3|5|6|7|8|9|10, 15|2|3|4|6|7|8|9|10, 1|25|3|4|6|7|8|9|10, 16|2|3|4|5|7|8|9|10, 1|26|3|4|5|7|8|9|10, 1|2|36|4|5|7|8|9|10, 17|2|3|4|5|6|8|9|10, 1|27|3|4|5|6|8|9|10, 1|2|37|4|5|6|8|9|10, 1|2|3|47|5|6|8|9|10, 18|2|3|4|5|6|7|9|10, 1|28|3|4|5|6|7|9|10, 1|2|38|4|5|6|7|9|10, 1|2|3|48|5|6|7|9|10, 1|2|3|4|58|6|7|9|10, 1|29|3|4|5|6|7|8|10, 1|2|39|4|5|6|7|8|10, 1|2|3|49|5|6|7|8|10, 1|2|3|4|59|6|7|8|10, 1|2|3|4|5|69|7|8|10, 1|2|3,10|4|5|6|7|8|9, 1|2|3|4,10|5|6|7|8|9, 1|2|3|4|5,10|6|7|8|9, 1|2|3|4|5|6,10|7|8|9, 1|2|3|4|5|6|7,10|8|9.

Crossrefs

Column k=9 of A261477.

Sequence in context: A094190 A069396 A228216 * A125482 A306322 A344733

Adjacent sequences: A261482 A261483 A261484 * A261486 A261487 A261488

Keyword

nonn,easy

Author

Alois P. Heinz, Aug 20 2015

Status

approved