A227589 Maximum label within a minimal labeling of n identical 4-sided dice yielding the most possible sums.

1, 4, 7, 12, 16, 23, 29, 38, 46, 57, 67, 80, 92, 107, 121, 138, 154, 173, 191, 212, 232

Offset: 0

Author

Jens Voß, Jul 17 2013

Keywords

• nonn
• more

Examples

			Three tetrahedra labeled (1, 2, 8, 12) yield the 20 possible sums 3, 4, 5, 6, 10, 11, 12, 14, 15, 16, 17, 18, 21, 22, 24, 25, 26, 28, 32, 36. No more sums can be obtained by different labelings, and no labeling with labels < 12 yields 20 possible sums. Therefore a(3) = 12.
		

Crossrefs

Row n=4 of array A227588.

Formula

Conjecture: a(n) = (n^2 + 3n + 5 - (-1)^n)/2 for n > 1.

Conjecture: a(n) = 2*a(n-1)-2*a(n-3)+a(n-4) for n>5. G.f.: (x^5-x^4-x^2+2*x+1) / ((x-1)^3*(x+1)). - Colin Barker, Aug 01 2013