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A099197 Figurate numbers based on the 10-dimensional regular convex polytope called the 10-dimensional cross-polytope, or 10-dimensional hyperoctahedron, which is represented by the Schlaefli symbol {3, 3, 3, 3, 3, 3, 3, 3, 4}. It is the dual of the 10-dimensional hypercube. 10
0, 1, 20, 201, 1360, 7001, 29364, 104881, 329024, 927441, 2390004, 5707449, 12767184, 26986089, 54284244, 104535009, 193664256, 346615329, 601446996, 1014889769, 1669752016, 2684641785, 4226553716, 6526963345, 9902174016, 14778775025, 21725194036, 31490462745 (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., Mar 12 2004, circulated by e-mail.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from T. D. Noe)

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.

J. V. Post, Math Pages.

Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

FORMULA

a(n) = 10-crosspolytope(n) = (n^2)*(2*n^8+120*n^6+1806*n^4+7180*n^2+5067)/14175.

G.f.: x*(1+x)^9/(1-x)^11. - Colin Barker, May 01 2012

a(n) = 20*a(n-1)/(n-1) + a(n-2) for n > 1. - Seiichi Manyama, Jun 06 2018

EXAMPLE

a(5) = 7001 because 10-crosspolytope(5) = (5^2)*(2*5^8 + 120*5^6 + 1806*5^4 + 7180*5^2 + 5067)/14175 = 7001, but there is no a priori way to expect that 10-crosspolytope(5) is prime.

PROG

(PARI) a(n)=n^2*(2*n^8+120*n^6+1806*n^4+7180*n^2+5067)/14175 \\ Charles R Greathouse IV, Oct 16 2015

CROSSREFS

Similar sequence: A005900 (m=3), A014820(n-1) (m=4), A069038 (m=5), A069039 (m=6), A099193 (m=7), A099195 (m=8), A099196 (m=9).

Cf. A000332.

Sequence in context: A120796 A120787 A223753 * A041766 A121088 A302838

Adjacent sequences:  A099194 A099195 A099196 * A099198 A099199 A099200

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Nov 16 2004

STATUS

approved

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Last modified May 25 19:11 EDT 2019. Contains 323576 sequences. (Running on oeis4.)