A071171 L_2 norm of vertices of Permuto-Associahedron in R^n.

0, 0, 5, 122, 1022, 5122, 18847, 56332, 144924, 332844, 699369, 1367894, 2522234, 4426526, 7449091, 12090616, 19017016, 29097336, 43447053, 63477138, 90949238, 128037338, 177396263, 242237380, 326411860, 434501860, 571919985, 745017390

Offset

0,3

References

G. M. Ziegler, Lectures on Polytopes, Springer-Verlag, NY, 1995, p. 311.

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Formula

a(n) = binomial(n+1, 3)*(30*n^4-33*n^2+2)/70.

G.f.: (5*x^2+82*x^3+186*x^4+82*x^5+5*x^6)/(1-x)^8.

Example

For n=3, the vertices are (9,5,4) and (8,7,3) of norm 122.

Mathematica

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 *)

Prog

(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 */

Crossrefs

Sequence in context: A290167 A193479 A324089 * A113906 A264456 A267914

Adjacent sequences: A071168 A071169 A071170 * A071172 A071173 A071174

Keyword

nonn,easy

Author

Michael Somos, Jun 10 2002

Status

approved