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A099196 Figurate numbers based on the 9-dimensional regular convex polytope called the 9-dimensional cross-polytope, or 9-dimensional hyperoctahedron, which is represented by the Schlaefli symbol {3, 3, 3, 3, 3, 3, 3, 4}. It is the dual of the 9-dimensional hypercube. 12
0, 1, 18, 163, 996, 4645, 17718, 57799, 166344, 432073, 1030490, 2286955, 4772780, 9446125, 17852030, 32398735, 56730512, 96220561, 158611106, 254831667, 400030580, 614859189, 927052742, 1373356887, 2001853784, 2874747225, 4071671786, 5693596923, 7867403068, 10751213181 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

H. S. M. Coxeter, Regular Polytopes, New York: Dover, 1973.

J. V. Post, "4-Dimensional Jonathan numbers: polytope numbers and Centered polytope numbers of Higher Than 3 Dimensions", Draft 1.5 of 9 a.m., 12 March 2004, circulated by e-mail.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Hyun Kwang Kim, On Regular Polytope Numbers, Proc. Amer. Math. Soc., 131 (2003), 65-75.

J. V. Post, Table of polytope numbers, Sorted, Through 1,000,000.

Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

FORMULA

a(n) = 9-crosspolytope(n) = n*(2*n^8 + 84*n^6 + 798*n^4 + 1636*n^2 + 315)/2835.

G.f.: x*(1+x)^8/(1-x)^10. [Colin Barker, May 01 2012]

a(n) = 18*a(n-1)/(n-1) + a(n-2) for n > 1. - Seiichi Manyama, Jun 06 2018

EXAMPLE

a(20) = 400030580 because 9-crosspolytope(20) = 20*(2*20^8 + 84*20^6 + 798*20^4 + 1636*20^2 + 315)/2835 = 400030580.

PROG

(PARI) concat(0, Vec(x*(1+x)^8/(1-x)^10 + O(x^40))) \\ Michel Marcus, Dec 14 2015

CROSSREFS

Similar sequence: A005900 (m=3), A014820(n-1) (m=4), A069038 (m=5), A069039 (m=6), A099193 (m=7), A099195 (m=8), A099197 (m=10).

Cf. A000332.

Sequence in context: A271899 A128797 A008418 * A041618 A055915 A208827

Adjacent sequences:  A099193 A099194 A099195 * A099197 A099198 A099199

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Nov 16 2004

EXTENSIONS

More terms from Michel Marcus, Dec 14 2015

STATUS

approved

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Last modified February 19 16:54 EST 2019. Contains 320311 sequences. (Running on oeis4.)