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A316584
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Array read by antidiagonals: T(n,k) is the number of elements x in GL(2,Z_n) with x^k == I mod n where I is the identity matrix.
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2
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1, 1, 1, 1, 4, 1, 1, 3, 14, 1, 1, 4, 9, 28, 1, 1, 1, 20, 9, 32, 1, 1, 6, 1, 64, 21, 56, 1, 1, 1, 30, 1, 184, 27, 58, 1, 1, 4, 1, 60, 25, 80, 171, 176, 1, 1, 3, 32, 1, 72, 1, 100, 33, 110, 1, 1, 4, 9, 64, 1, 180, 1, 640, 297, 128, 1, 1, 1, 14, 9, 224, 1, 846, 1, 164, 63, 134, 1
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OFFSET
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1,5
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COMMENTS
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All columns are multiplicative.
Some terms of this sequence may also be computed using a formula given by Kent Morrison (section 1.11 and 2.5 in the reference). See A053725 for a PARI implementation.
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LINKS
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FORMULA
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Conjecture: T(p,p) = p^2 for p prime.
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EXAMPLE
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Array begins:
======================================================
n\k | 1 2 3 4 5 6 7 8 9 10
------+-----------------------------------------------
1 | 1 1 1 1 1 1 1 1 1 1 ...
2 | 1 4 3 4 1 6 1 4 3 4 ...
3 | 1 14 9 20 1 30 1 32 9 14 ...
4 | 1 28 9 64 1 60 1 64 9 28 ...
5 | 1 32 21 184 25 72 1 224 21 80 ...
6 | 1 56 27 80 1 180 1 128 27 56 ...
7 | 1 58 171 100 1 846 49 184 171 58 ...
8 | 1 176 33 640 1 432 1 1024 33 176 ...
9 | 1 110 297 164 1 1566 1 272 729 110 ...
10 | 1 128 63 736 25 432 1 896 63 320 ...
11 | 1 134 111 244 1325 354 1 464 111 5950 ...
12 | 1 392 81 1280 1 1800 1 2048 81 392 ...
13 | 1 184 549 1096 1 2736 469 1408 549 184 ...
14 | 1 232 513 400 1 5076 49 736 513 232 ...
15 | 1 448 189 3680 25 2160 1 7168 189 1120 ...
...
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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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