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Search: id:A072229
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| A072229 |
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Witt index of the standard bilinear form <1,1,1,...,1> over the 2-adic rationals. |
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+0
1
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| 0, 0, 0, 0, 1, 2, 3, 4, 4, 4, 4, 5, 6, 7, 8, 8, 8, 8, 9, 10, 11, 12, 12, 12, 12, 13, 14, 15, 16, 16, 16, 16, 17, 18, 19, 20, 20, 20, 20, 21, 22, 23, 24, 24, 24, 24, 25, 26, 27, 28, 28, 28, 28, 29, 30, 31, 32, 32, 32, 32, 33, 34, 35, 36, 36, 36, 36, 37, 38, 39, 40, 40, 40, 40, 41, 42
(list; graph; listen)
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OFFSET
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0,6
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COMMENT
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There is another interesting bilinear form over Q_2 : it is <1, ..., 1, 2>. It has Witt index 0, 0, 0, 1, 1, 2, 3, 3, 4, 4, 4, 5, 5, 6, 7, 7...
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FORMULA
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a(n) = 4 floor(n/7) + [0,0,0,0,1,2,3][n%7 + 1]. (Formula corrected by Franklin T. Adams-Watters, Apr 13 2009)
a(n)=a(n-1)+a(n-7)-a(n-8). G.f.: x^4*(1+x)*(1+x^2)/((x^6+x^5+x^4+x^3+x^2+x+1)*(x-1)^2). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 16 2009]
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MAPLE
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for n from 0 to 120 do printf("%d, ", 4*floor(n/7)+op( (n mod 7)+1, [0, 0, 0, 0, 1, 2, 3]) ) ; od: [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 16 2009]
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CROSSREFS
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Sequence in context: A087848 A087844 A140427 this_sequence A120509 A029106 A064004
Adjacent sequences: A072226 A072227 A072228 this_sequence A072230 A072231 A072232
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KEYWORD
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nonn,nice,easy
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AUTHOR
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G. Collinet (collinet(AT)math.polytechnique.fr), Jul 05 2002
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 16 2009
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