A346911 - OEIS

%I #14 Sep 11 2021 01:11:43

%S 2,4,6,6,15,8,8,28,32,16,10,45,80,80,32,12,66,160,240,192,64,14,91,

%T 280,560,672,448,128,16,120,448,1120,1792,1792,1024,256,18,153,672,

%U 2016,4032,5376,4608,2304,512

%N Triangle read by rows: T(n,k) is the number of k-dimensional simplices with vertices from the n-dimensional cross polytope; 0 <= k < n.

%F T(n,0) = 2*n;

%F T(n,1) = 2*n^2-n;

%F T(n,k) = A013609(n,k+1) when k > 1.

%e Table begins:

%e n\k |  0    1    2     3     4     5     6     7    8

%e ----+-------------------------------------------------

%e   1 |  2

%e   2 |  4,   6

%e   3 |  6,  15,   8

%e   4 |  8,  28,  32,   16

%e   5 | 10,  45,  80,   80,   32

%e   6 | 12,  66, 160,  240,  192,   64

%e   7 | 14,  91, 280,  560,  672,  448,  128

%e   8 | 16, 120, 448, 1120, 1792, 1792, 1024,  256

%e   9 | 18, 153, 672, 2016, 4032, 5376, 4608, 2304, 512

%e Three of the T(3,1) = 15 1-simplices (line segments) in the 3-dimensional cross-polytope have vertices {(1,0,0), (-1,0,0)}, {(1,0,0), (0,1,0)}, and {(0,1,0), (0,0,-1)}.

%e One of the T(5,3) = 80 of the 3-simplices (tetrahedra) in the 5-dimensional cross-polytope has vertices {(1,0,0,0,0), (0,0,1,0,0), (0,0,0,-1,0), (0,0,0,0,1)}.

%Y Cf. A013609, A346905.

%K nonn,tabl,more

%O 1,1

%A _Peter Kagey_, Aug 06 2021