A392318 Decimal expansion of 37/72.

5, 1, 3, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8

Offset

0,1

Comments

If three fair six-sided dice are rolled, the probability that the numbers obtained can be the side lengths of a triangle is 37/72.

When three dice are rolled, there are 6^3 = 216 triples (a, b, c) with 1 <= a, b, c < = 6. Among these, exactly 111 triples satisfy the triangle inequalities: a + b > c, b + c > a and a + c > b. Hence the probability is 111/216 = 37/72 > 1/2.

Among the 111 admissible triples, 42 correspond to scalene triangles, 63 triangles with exactly two equal sides and 6 to equilateral triangles.

Links

Table of n, a(n) for n=0..86.

Index entries for linear recurrences with constant coefficients, signature (1).

Formula

G.f.: (5 - 4*x + 2*x^2 + 5*x^3)/(1 - x). - Stefano Spezia, Jan 08 2026

Example

37/72 = 0.513888888...

Mathematica

RealDigits[37/72, 10, 100][[1]]

Crossrefs

Cf. A021220 (1/216).

Sequence in context: A074048 A394506 A244350 * A176321 A248130 A365457

Adjacent sequences: A392315 A392316 A392317 * A392319 A392320 A392321

Keyword

nonn,cons,easy

Author

Gonzalo Martínez, Jan 06 2026

Status

approved