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

0,2

Links

Table of n, a(n) for n=0..20.

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

Example

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.

Sequence in context: A310782 A232424 A005005 * A310783 A310784 A310785

Adjacent sequences: A227586 A227587 A227588 * A227590 A227591 A227592

Keyword

nonn,more

Author

Jens Voß, Jul 17 2013

Status

approved