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A294053 Number of set partitions of [n] such that the maximal absolute difference between consecutive elements within a block equals four. 2
5, 38, 215, 1061, 4835, 20973, 88010, 360787, 1453978, 5784863, 22790024, 89092968, 346161413, 1338360327, 5153828402, 19781784669, 75723483993, 289218958150, 1102597884045, 4196961350447, 15954736073286, 60585891849501, 229855881578197, 871373727460242 (list; graph; refs; listen; history; text; internal format)
OFFSET
5,1
LINKS
Index entries for linear recurrences with constant coefficients, signature (9,-26,23,0,20,-40,2,16,-1,0,-3,1)
FORMULA
G.f.: (x^5-2*x^4+x^3-3*x^2+7*x-5)*x^5 / ((x-1) *(x^3-x^2-3*x+1) *(x^8 -x^7 -7*x^5 +7*x^4 +x^3 +4*x^2 -5*x+1)).
a(n) = A287276(n) - A287275(n).
MATHEMATICA
Drop[CoefficientList[Series[(x^5-2x^4+x^3-3x^2+7x-5)x^5/((x-1)(x^3-x^2- 3x+1)(x^8-x^7-7x^5+7x^4+x^3+4x^2-5x+1)), {x, 0, 30}], x], 5] (* or *) LinearRecurrence[{9, -26, 23, 0, 20, -40, 2, 16, -1, 0, -3, 1}, {5, 38, 215, 1061, 4835, 20973, 88010, 360787, 1453978, 5784863, 22790024, 89092968}, 30] (* Harvey P. Dale, May 25 2022 *)
CROSSREFS
Column k=4 of A287213.
Sequence in context: A145156 A318102 A163698 * A345686 A279265 A129048
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Oct 22 2017
STATUS
approved

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Last modified February 23 09:02 EST 2024. Contains 370276 sequences. (Running on oeis4.)