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A250002
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Triangle read by rows: T(n,k) = number of inequivalent binary linear [n,k] codes minus C(n,k).
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2
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 2, 8, 8, 2, 0, 0, 0, 0, 4, 21, 36, 21, 4, 0, 0, 0, 0, 7, 47, 114, 114, 47, 7, 0, 0, 0, 0, 11, 93, 306, 453, 306, 93, 11, 0, 0, 0, 0, 16, 168, 730, 1526, 1526, 730, 168, 16, 0, 0
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refs;
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OFFSET
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0,25
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COMMENTS
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The triangle of inequivalent binary linear [n,k] codes (A076831) looks much like Pascal's triangle (A007318). They start to differ in the middle of row 6. This triangle is the difference between them. Its row sums are A250003 - the difference between the numbers of inequivalent binary linear codes of length n (A076766) and the powers of two (A000079).
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LINKS
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FORMULA
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EXAMPLE
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k 0 1 2 3 4 5 6 7 8 9 10 11 sums
n
0 0 0
1 0 0 0
2 0 0 0 0
3 0 0 0 0 0
4 0 0 0 0 0 0
5 0 0 0 0 0 0 0
6 0 0 1 2 1 0 0 4
7 0 0 2 8 8 2 0 0 20
8 0 0 4 21 36 21 4 0 0 86
9 0 0 7 47 114 114 47 7 0 0 336
10 0 0 11 93 306 453 306 93 11 0 0 1273
11 0 0 16 168 730 1526 1526 730 168 16 0 0 4880
Row 6 of A076831 is (1,6,16,22,16,6,1) and row 6 of A007318 is (1,6,15,20,15,6,1). Row 6 of this triangle is their difference (0,0,1,2,1,0,0).
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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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