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Search: id:A123067
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| A123067 |
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Theta series of the "Little Methuselah" quadratic form x^2 + 2*y^2 + y*z + 4*z^2. |
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4
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| 1, 2, 2, 4, 4, 6, 8, 2, 10, 10, 2, 12, 4, 4, 10, 4, 10, 12, 10, 10, 20, 12, 4, 12, 12, 12, 8, 8, 8, 24, 8, 0, 24, 12, 8, 10, 24, 12, 6, 12, 14, 38, 8, 8, 32, 18, 8, 4, 8, 20, 20, 16, 12, 16, 24, 4, 30, 28, 4, 14, 20, 12, 2, 18, 18, 44, 20, 8, 28, 12, 10, 26, 30, 12, 28, 16, 20, 20, 8, 16, 34
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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The Little Methuselah form represents every integer from 1 to 30, but fails to represent 31. Every integer-valued positive definite ternary form not equivalent to it fails to represent some integer between 1 and 30. [Conway]
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REFERENCES
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J. H. Conway, The Sensual (Quadratic) Form, M.A.A., 1997, pp. 81-82.
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EXAMPLE
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1+2*x+2*x^2+4*x^3+4*x^4+6*x^5+8*x^6+2*x^7+10*x^8+10*x^9+2*x^10+...
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PROGRAM
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(MAGMA) L:=LatticeWithGram(3, [2, 0, 0, 0, 4, 1, 0, 1, 8] ); T<q> := ThetaSeries(L, 500); T;
(PARI) {a(n)= if(n<1, n==0, qfrep([2, 0, 0; 0, 4, 1; 0, 1, 8], n, 1)[n]*2)} /* Michael Somos Oct 23 2006 */
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CROSSREFS
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Cf. A123063, A123064, A123065, A123068.
Sequence in context: A067590 A027188 A089076 this_sequence A057601 A087135 A094858
Adjacent sequences: A123064 A123065 A123066 this_sequence A123068 A123069 A123070
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KEYWORD
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nonn
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AUTHOR
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njas, Sep 27 2006, corrected Oct 26 2006
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