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A096337 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. 2
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; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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.

a(n) is the number of nonempty multisets of positive integers < n such that their sum modulo n is zero and that no proper nonempty subset has this property. - George B. Salomon, Sep 29 2019

LINKS

Table of n, a(n) for n=1..39.

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.

Klaus Pommerening, The Indecomposable Solutions of Linear Congruences, arXiv:1703.03708 [math.NT], 2017.

EXAMPLE

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.

CROSSREFS

Sequence in context: A097633 A263620 A083356 * A175318 A281025 A109757

Adjacent sequences:  A096334 A096335 A096336 * A096338 A096339 A096340

KEYWORD

nonn

AUTHOR

Mamuka Jibladze, Jun 28 2004

STATUS

approved

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Last modified May 9 12:48 EDT 2021. Contains 343740 sequences. (Running on oeis4.)