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A347970
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Triangle read by rows: T(n, k) is the number of k-dimensional subspaces in (F_3)^n, counted up to coordinate permutation (n >= 0, 0 <= k <= n).
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3
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1, 1, 1, 1, 3, 1, 1, 5, 5, 1, 1, 8, 16, 8, 1, 1, 11, 39, 39, 11, 1, 1, 15, 87, 168, 87, 15, 1, 1, 19, 176, 644, 644, 176, 19, 1, 1, 24, 338, 2348, 4849, 2348, 338, 24, 1, 1, 29, 613, 8137, 37159, 37159, 8137, 613, 29, 1, 1, 35, 1071, 27047, 286747, 679054, 286747, 27047, 1071
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OFFSET
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0,5
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COMMENTS
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Columns can be computed by a method analogous to that of Fripertinger for isometry classes of linear codes, disallowing scalar transformation of individual coordinates.
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LINKS
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EXAMPLE
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Triangle begins:
k: 0 1 2 3 4 5 6 7
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n=0: 1
n=1: 1 1
n=2: 1 3 1
n=3: 1 5 5 1
n=4: 1 8 16 8 1
n=5: 1 11 39 39 11 1
n=6: 1 15 87 168 87 15 1
n=7: 1 19 176 644 644 176 19 1
There are 4 = A022167(2, 1) one-dimensional subspaces in (F_3)^2, namely, those generated by (0, 1), (1, 0), (1, 1), and (1, 2). The first two are related by coordinate swap, while the remaining two are invariant. Hence, T(2, 1) = 3.
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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