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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 September 26 05:53 EDT 2022. Contains 356986 sequences. (Running on oeis4.)