|
%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
|
