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Search: id:A125501
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| A125501 |
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The (1,1)-entry in the matrix M^n, where M is the 7 X 7 Cartan matrix [2,-1,0,0,0,0,0; -1,2,-1,0,0,0,0; 0,-1,2,-1,0,0,-1; 0,0,-1,2,-1,0,0; 0,0,0,-1,2,-1,0; 0,0,0,0,-1,2,0; 0,0,-1,0,0,0,2]. |
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+0
1
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| 1, 2, 5, 14, 42, 132, 430, 1444, 4981, 17594, 63442, 232828, 867145, 3269034, 12446307, 47767466, 184508963, 716386598, 2793067210, 10926148172, 42857189054, 168471757292, 663434825367, 2616336659586, 10329939578230
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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Wikipedia (E_7, Mathematics).
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EXAMPLE
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a(6) = 430 = leftmost term in M^6 * [1,0,0,0,0,0,0].
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MAPLE
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with(linalg): M[1]:=matrix(7, 7, [2, -1, 0, 0, 0, 0, 0, -1, 2, -1, 0, 0, 0, 0, 0, -1, 2, -1, 0, 0, -1, 0, 0, -1, 2, -1, 0, 0, 0, 0, 0, -1, 2, -1, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, -1, 0, 0, 0, 2]): for n from 2 to 30 do M[n]:=multiply(M[1], M[n-1]) od:1, seq(M[n][1, 1], n=1..30); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 20 2007
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PROGRAM
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(PARI) {a(n)=local(E7=[2, -1, 0, 0, 0, 0, 0; -1, 2, -1, 0, 0, 0, 0; 0, -1, 2, -1, 0, 0, -1; 0, 0, -1, 2, -1, 0, 0; 0, 0, 0, -1, 2, -1, 0; 0, 0, 0, 0, -1, 2, 0; 0, 0, -1, 0, 0, 0, 2]); (E7^n)[1, 1]} - Paul D. Hanna (pauldhanna(AT)juno.com), Jan 02 2007
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CROSSREFS
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Cf. A126566, A126567, A126569.
Sequence in context: A120588 A057413 A126567 this_sequence A126569 A162748 A061815
Adjacent sequences: A125498 A125499 A125500 this_sequence A125502 A125503 A125504
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KEYWORD
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nonn
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 28 2006
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EXTENSIONS
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More terms from Paul D. Hanna (pauldhanna(AT)juno.com), Jan 02 2007
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