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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.
2
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
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: A319890 A319871 A374506 * A215226 A349427 A200864
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Aug 20 2015
STATUS
approved