cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A294053 Number of set partitions of [n] such that the maximal absolute difference between consecutive elements within a block equals four.

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%I A294053 #9 May 25 2022 17:48:37
%S A294053 5,38,215,1061,4835,20973,88010,360787,1453978,5784863,22790024,
%T A294053 89092968,346161413,1338360327,5153828402,19781784669,75723483993,
%U A294053 289218958150,1102597884045,4196961350447,15954736073286,60585891849501,229855881578197,871373727460242
%N A294053 Number of set partitions of [n] such that the maximal absolute difference between consecutive elements within a block equals four.
%H A294053 Alois P. Heinz, <a href="/A294053/b294053.txt">Table of n, a(n) for n = 5..1000</a>
%H A294053 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (9,-26,23,0,20,-40,2,16,-1,0,-3,1)
%F A294053 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)).
%F A294053 a(n) = A287276(n) - A287275(n).
%t A294053 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 *)
%Y A294053 Column k=4 of A287213.
%Y A294053 Cf. A287275, A287276.
%K A294053 nonn,easy
%O A294053 5,1
%A A294053 _Alois P. Heinz_, Oct 22 2017