A008501 - OEIS

%I #29 Sep 08 2022 08:44:35

%S 1,9,45,165,495,1287,3003,6435,12869,24301,43713,75417,125475,202203,

%T 316767,483879,722601,1057265,1518517,2144493,2982135,4088655,5533155,

%U 7398411,9782829,12802581,16593929

%N 7-dimensional centered tetrahedral numbers.

%C 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

%H Vincenzo Librandi, <a href="/A008501/b008501.txt">Table of n, a(n) for n = 0..10000</a>

%H Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Two Enumerative Functions</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1).

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

%F 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

%p seq(binomial(n+8,8) - binomial(n,8), n=0..30); # _G. C. Greubel_, Nov 09 2019

%t Table[Binomial[n + 8, 8] - Binomial[n, 8], {n, 0, 26}] (* _Bruno Berselli_, Mar 22 2012 *)

%o (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

%o (PARI) vector(31, n, b=binomial; b(n+7,8) - b(n-1,8) ) \\ _G. C. Greubel_, Nov 09 2019

%o (Sage) b=binomial; [b(n+8,8) - b(n,8) for n in (0..30)] # _G. C. Greubel_, Nov 09 2019

%o (GAP) B:=Binomial;; List([0..30], n-> B(n+8,8)-B(n,8) ); # _G. C. Greubel_, Nov 09 2019

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_