A131514 - OEIS

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A131514

Number of ways to design a set of three n-sided dice (using nonnegative numbers) such that summing the faces can give any integer number from 0 to n^3-1.

1, 1, 1, 15, 1, 71, 1, 280, 15, 71, 1, 3660, 1, 71, 71 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,4`
	COMMENTS	`Also the number of ways to factor (x^(n^3)-1)/(x-1) into p(x)q(x)r(x), such that p(x),q(x),r(x) are polynomials with exactly n terms and all coefficients +1 (and all exponents nonnegative).`
	EXAMPLE	a(4)=15 because we can choose any of the following 15 configurations for our three dice: [{0, 1, 2, 3}, {0, 4, 8, 12}, {0, 16, 32, 48}], [{0, 1, 2, 3}, {0, 4, 16, 20}, {0, 8, 32, 40}], [{0, 1, 2, 3}, {0, 4, 32, 36}, {0, 8, 16, 24}], [{0, 1, 4, 5}, {0, 2, 8, 10}, {0, 16, 32, 48}], [{0, 1, 4, 5}, {0, 2, 16, 18}, {0, 8, 32, 40}], [{0, 1, 4, 5}, {0, 2, 32, 34}, {0, 8, 16, 24}], [{0, 1, 8, 9}, {0, 2, 4, 6}, {0, 16, 32, 48}], [{0, 1, 8, 9}, {0, 2, 16, 18}, {0, 4, 32, 36}], [{0, 1, 8, 9}, {0, 2, 32, 34}, {0, 4, 16, 20}], [{0, 1, 16, 17}, {0, 2, 4, 6}, {0, 8, 32, 40}], [{0, 1, 16, 17}, {0, 2, 8, 10}, {0, 4, 32, 36}], [{0, 1, 16, 17}, {0, 2, 32, 34}, {0, 4, 8, 12}], [{0, 1, 32, 33}, {0, 2, 4, 6}, {0, 8, 16, 24}], [{0, 1, 32, 33}, {0, 2, 8, 10}, {0, 4, 16, 20}], [{0, 1, 32, 33}, {0, 2, 16, 18}, {0, 4, 8, 12}]
	CROSSREFS	`Sequence in context: A201460 A040239 A126141 * A049327 A030527 A027467` `Adjacent sequences: A131511 A131512 A131513 * A131515 A131516 A131517`
	KEYWORD	`nonn`
	AUTHOR	`H.B. Wassenaar (towr(AT)ai.rug.nl), Aug 14 2007`

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Last modified February 14 22:07 EST 2012. Contains 205668 sequences.