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%I #17 Mar 15 2024 11:56:20
%S 0,0,5,122,1022,5122,18847,56332,144924,332844,699369,1367894,2522234,
%T 4426526,7449091,12090616,19017016,29097336,43447053,63477138,
%U 90949238,128037338,177396263,242237380,326411860,434501860,571919985,745017390
%N L_2 norm of vertices of Permuto-Associahedron in R^n.
%D G. M. Ziegler, Lectures on Polytopes, Springer-Verlag, NY, 1995, p. 311.
%H Harvey P. Dale, <a href="/A071171/b071171.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1).
%F a(n) = binomial(n+1, 3)*(30*n^4-33*n^2+2)/70.
%F G.f.: (5*x^2+82*x^3+186*x^4+82*x^5+5*x^6)/(1-x)^8.
%e For n=3, the vertices are (9,5,4) and (8,7,3) of norm 122.
%t Table[Binomial[n+1,3] (30n^4-33n^2+2)/70,{n,0,30}] (* or *) LinearRecurrence[ {8,-28,56,-70,56,-28,8,-1},{0,0,5,122,1022,5122,18847,56332},30] (* _Harvey P. Dale_, Dec 25 2020 *)
%o (PARI) {a(n) = polcoeff( (5*x^2 + 82*x^3 + 186*x^4 + 82*x^5 + 5*x^6) / (1 - x)^8 + x * O(x^n), n)} /* _Michael Somos_, Mar 04 2012 */
%K nonn,easy
%O 0,3
%A _Michael Somos_, Jun 10 2002
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