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Search: id:A123063
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| A123063 |
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Theta series of lattice with Gram matrix [4,1;1,8]. |
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+0
5
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| 1, 0, 2, 0, 2, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 0, 4, 0, 2, 2, 4, 0, 0, 0, 0, 2, 0, 0, 4, 0, 0, 0, 4, 0, 0, 2, 2, 0, 2, 0, 6, 2, 0, 0, 0, 2, 0, 0, 0, 2, 4, 0, 0, 0, 0, 0, 6, 0, 0, 2, 0, 0, 2, 2, 4, 0, 0, 0, 0, 0, 6, 2, 2, 0, 0, 0, 4, 0, 0, 0, 6, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 4, 2, 0, 2, 4, 0, 6, 2, 0, 2, 0
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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J. H. Conway, The Sensual (Quadratic) Form, M.A.A., 1997, p. 82.
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FORMULA
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G.f. A(x) satisfies 0=f(A(x), A(x^2), A(x^3), A(x^6)) where f(u1, u2, u3, u6)= +u6*u1^3 +2*u3*u2^3 -3*u3^3*u2 -6*u6^3*u1 +6*u6*u2^2*u1 -6*u3*u2^2*u1 +3*u3*u2*u1^2 -6*u6*u2*u1^2 -9*u6*u3^2*u1 -18*u6^2*u3*u2 +18*u6*u3^2*u2 +18*u6^2*u3*u1 . - Michael Somos Sep 28 2006
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EXAMPLE
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1 + 2*q^4 + 2*q^8 + 2*q^10 + 2*q^14 + 2*q^16 + 2*q^20 + 2*q^28 + 4*q^32 + 2*q^36 + ...
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PROGRAM
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(MAGMA) L:=LatticeWithGram(2, [4, 1, 1, 8] ); T<q> := ThetaSeries(L, 500); T;
(PARI) {a(n)=if(n<1, n==0, qfrep([4, 1; 1, 8], n, 1)[n]*2)} /* Michael Somos Sep 28 2006 */
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CROSSREFS
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Cf. A123064, A123065.
Sequence in context: A088627 A024713 A123530 this_sequence A031358 A029317 A127800
Adjacent sequences: A123060 A123061 A123062 this_sequence A123064 A123065 A123066
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KEYWORD
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nonn
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AUTHOR
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njas, Sep 27 2006
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