A008501 7-dimensional centered tetrahedral numbers.

1, 9, 45, 165, 495, 1287, 3003, 6435, 12869, 24301, 43713, 75417, 125475, 202203, 316767, 483879, 722601, 1057265, 1518517, 2144493, 2982135, 4088655, 5533155, 7398411, 9782829, 12802581, 16593929

Offset

0,2

Comments

If X is an n-set and Y a fixed 8-subset of X then a(n-8) is equal to the number of 8-subsets of X intersecting Y. - Milan Janjic, Jul 30 2007

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Milan Janjic, Two Enumerative Functions

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

Formula

G.f.: (1-x^8)/(1-x)^9 = (1+x)*(1+x^2)*(1+x^4)/(1-x)^8.

1260*a(n) = (2*n+1)*(n^6 + 3*n^5 + 100*n^4 + 195*n^3 + 1159*n^2 + 1062*n + 1260). - R. J. Mathar, Mar 14 2011

Maple

seq(binomial(n+8, 8) - binomial(n, 8), n=0..30); # G. C. Greubel, Nov 09 2019

Mathematica

Table[Binomial[n + 8, 8] - Binomial[n, 8], {n, 0, 26}] (* Bruno Berselli, Mar 22 2012 *)

Prog

(Magma) [((2*n+1)*(n^6+3*n^5 +100*n^4 +195*n^3 +1159*n^2 +1062*n +1260)/1260) : n in [0..30]]; // Vincenzo Librandi, Oct 08 2011
(PARI) vector(31, n, b=binomial; b(n+7, 8) - b(n-1, 8) ) \\ G. C. Greubel, Nov 09 2019
(Sage) b=binomial; [b(n+8, 8) - b(n, 8) for n in (0..30)] # G. C. Greubel, Nov 09 2019
(GAP) B:=Binomial;; List([0..30], n-> B(n+8, 8)-B(n, 8) ); # G. C. Greubel, Nov 09 2019

Crossrefs

Sequence in context: A162602 A247609 A341138 * A341206 A306942 A289354

Adjacent sequences: A008498 A008499 A008500 * A008502 A008503 A008504

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved