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A270227
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Array read by antidiagonals: T(n,m) = number of matchings (i.e., Hosoya index) in K_n X K_m.
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8
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1, 2, 2, 4, 7, 4, 10, 32, 32, 10, 26, 193, 370, 193, 26, 76, 1382, 5950, 5950, 1382, 76, 232, 11719, 122984, 270529, 122984, 11719, 232, 764, 112604, 3175696, 16873930, 16873930, 3175696, 112604, 764, 2620, 1221889, 98815588, 1384880065, 3337807996, 1384880065, 98815588, 1221889, 2620
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OFFSET
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1,2
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COMMENTS
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Observations: (for n+m <= 32)
Examination of values modulus a small prime yields several patterns.
T(n,m) == (n+1)*(m+1) (mod 2) for n+m>2.
T(n,m) == T(n,m+6) (mod 3).
T(n,m) is not divisible by 3.
T(n,m) == 0 (mod 5) for n==4 (mod 5) and m<>2 and except when m=n=4.
T(5,m) == 0 (mod 208) for m >= 13.
T(6,m) == 0 (mod 19) for m >= 19.
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LINKS
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Eric Weisstein's World of Mathematics, Matching
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EXAMPLE
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The start of the sequence as table:
* 1 2 4 10 26 76 ...
* 2 7 32 193 1382 11719 ...
* 4 32 370 5950 122984 3175696 ...
* 10 193 5950 270529 16873930 1384880065 ...
* 26 1382 122984 168739305 3337807996 909046586596 ...
* 76 11719 3175696 1384880065 909046586596 855404716021831 ...
* ...
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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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