A346911 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.

2, 4, 6, 6, 15, 8, 8, 28, 32, 16, 10, 45, 80, 80, 32, 12, 66, 160, 240, 192, 64, 14, 91, 280, 560, 672, 448, 128, 16, 120, 448, 1120, 1792, 1792, 1024, 256, 18, 153, 672, 2016, 4032, 5376, 4608, 2304, 512

Offset

1,1

Links

Table of n, a(n) for n=1..45.

Formula

T(n,0) = 2*n;

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

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

Example

Table begins:
n\k |  0    1    2     3     4     5     6     7    8
----+-------------------------------------------------
  1 |  2
  2 |  4,   6
  3 |  6,  15,   8
  4 |  8,  28,  32,   16
  5 | 10,  45,  80,   80,   32
  6 | 12,  66, 160,  240,  192,   64
  7 | 14,  91, 280,  560,  672,  448,  128
  8 | 16, 120, 448, 1120, 1792, 1792, 1024,  256
  9 | 18, 153, 672, 2016, 4032, 5376, 4608, 2304, 512
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)}.
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)}.

Crossrefs

Cf. A013609, A346905.

Sequence in context: A278227 A104968 A286894 * A225187 A281485 A142473

Adjacent sequences: A346908 A346909 A346910 * A346912 A346913 A346914

Keyword

nonn,tabl,more

Author

Peter Kagey, Aug 06 2021

Status

approved