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Search: id:A096337
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| A096337 |
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Number of those nonnegative integer solutions of the congruence x_1+2x_2+...+(n-1)x_{n-1} = 0 (mod n) which are indecomposable, that is, are not nonnegative linear combinations of other nonnegative integer solutions. |
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+0
1
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| 0, 1, 3, 6, 14, 19, 47, 64, 118, 165, 347, 366, 826, 973, 1493, 2134, 3912, 4037, 7935, 8246, 12966, 17475, 29161, 28064, 49608, 59357, 83419, 97242, 164966, 152547, 280351, 295290, 405918, 508161, 674629, 708818, 1230258, 1325731, 1709229
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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a(n) is a lower bound for the number of fundamental invariants of binary forms of degree n+2 - see Kac. A lower estimate for a(n) is given by Dixmier et al.
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REFERENCES
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J. Dixmier, P. Erdos and J.-L. Nicolas, ``Sur le nombre d'invariants fondamentaux des formes binaires'', C. R. Acad. Sci. Paris Ser. I Math. 305 (1987), no. 8, 319-322.
V. Kac, ``Root systems, representations of quivers and invariant theory'', Invariant theory (Montecatini, 1982), 74-108, Lecture Notes in Math., 996, Springer, Berlin, 1983.
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EXAMPLE
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a(3)=3 since 3+2*0=3, 1+2*1=3 and 0+2*3=6 are the only indecomposable nonnegative integer solutions to x_1+2x_2=0 (mod 3): all other nonnegative integer solutions have form x_1=p*3+q*1+r*0, x_2=p*0+q*1+r*3 for nonnegative integers p, q, r.
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CROSSREFS
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Adjacent sequences: A096334 A096335 A096336 this_sequence A096338 A096339 A096340
Sequence in context: A118523 A097633 A083356 this_sequence A109757 A075189 A093866
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KEYWORD
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nonn
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AUTHOR
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Mamuka Jibladze (jib(AT)rmi.acnet.ge), Jun 28 2004
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