A099195 a(n) = (n^2)*( n^6 + 28*n^4 + 154*n^2 + 132 )/315.

0, 1, 16, 129, 704, 2945, 10128, 29953, 78592, 187137, 411280, 845185, 1640640, 3032705, 5373200, 9173505, 15158272, 24331777, 38058768, 58161793, 87037120, 127791489, 184402064, 261902081, 366594816, 506298625, 690625936, 931299201, 1242506944, 1641303169, 2148053520

Offset: 0

Author

Jonathan Vos Post, Nov 16 2004

Keywords

• easy
• nonn

References

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

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• Milan Janjic and B. Petkovic, A Counting Function, arXiv 1301.4550 [math.CO], 2013.
• Milan Janjic and B. Petkovic, A Counting Function Generalizing Binomial Coefficients and Some Other Classes of Integers, J. Int. Seq. 17 (2014) # 14.3.5
• Hyun Kwang Kim, On Regular Polytope Numbers, Proc. Amer. Math. Soc., 131 (2003), 65-75.
• Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Crossrefs

Similar sequences: A005900 (m=3), A014820(n-1) (m=4), A069038 (m=5), A069039 (m=6), A099193 (m=7), A099196 (m=9), A099197 (m=10).

Cf. A000332.

Programs

Mathematica

LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{0,1,16,129,704,2945,10128,29953,78592},40] (* Harvey P. Dale, Jan 23 2019 *)

PARI

concat(0, Vec(x*(1+x)^7/(1-x)^9 + O(x^40))) \\ Michel Marcus, Dec 14 2015

Formula

a(n) = (n^2)*( n^6 + 28*n^4 + 154*n^2 + 132 )/315.

G.f.: x*(1+x)^7/(1-x)^9. [R. J. Mathar, Jul 18 2009]

a(n) = 16*a(n-1)/(n-1) + a(n-2) for n > 1. - Seiichi Manyama, Jun 06 2018