A261480 Number of set partitions of [n] into exactly four parts such that no part contains two elements with a circular distance less than three.

1, 0, 3, 7, 7, 21, 50, 77, 164, 364, 672, 1330, 2787, 5474, 10797, 21945, 43841, 87031, 174812, 350175, 698302, 1397550, 2798250, 5591460, 11181661, 22374660, 44740503, 89467147, 178965787, 357927801, 715796390, 1431659537, 2863370744, 5726556304, 11453194452

Offset

4,3

Links

Alois P. Heinz, Table of n, a(n) for n = 4..1000

Index entries for linear recurrences with constant coefficients, signature (0,1,5,4,-1,-4,-4).

Formula

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

Example

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

Crossrefs

Column k=4 of A261477.

Sequence in context: A157102 A226512 A270307 * A121172 A341539 A322934

Adjacent sequences: A261477 A261478 A261479 * A261481 A261482 A261483

Keyword

nonn,easy

Author

Alois P. Heinz, Aug 20 2015

Status

approved