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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.
0
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
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
Sequence in context: A278227 A104968 A286894 * A225187 A281485 A142473
KEYWORD
nonn,tabl,more
AUTHOR
Peter Kagey, Aug 06 2021
STATUS
approved