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The number of solutions, in this case 8, is given by A062011(6). Robert G. Wilson v, Apr 10 2019
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For values k>=0 this sequence gives the possible point scores in Australian Rules Football which equal the corresponding number of goals (worth six points) times the number of pointsbehinds (worth one point).
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In general if we replace 6 by n, then the number of solutions will be 2*A000005(n), the smallest lowest value will be -n*n + 2*(n - 1, )^2, and the largest highest value will be n*n + 2*(n + 1)^2.
The sequence can be found by solving the equality i * j = 6 * i + j. Re-arranging for j gives j = 6 + 6/(i-1). As both i and j must be integers this implies i - 1 must divide 6, thus the only values for i are -5,-2,-1,0,2,3,4,7. Finding the corresponding j and multiplying gives the 8 sequences values.
In general if we replace 6 by n, then the number of solutions will be 2*A000005(n), the smallest value will be -n*n + 2*n - 1, and the largest value will be n*n + 2*n + 1.
Cf. A000005