A258064 Number of hands of n points in Spanish dominoes.

3, 9, 29, 67, 147, 283, 526, 893, 1470, 2287, 3451, 4990, 7030, 9559, 12697, 16375, 20664, 25406, 30621, 36034, 41618, 47022, 52174, 56696, 60548, 63362, 65186, 65746, 65186, 63362, 60548, 56696, 52174, 47022, 41618, 36034, 30621, 25406, 20664, 16375, 12697, 9559, 7030, 4990, 3451, 2287, 1470, 893, 526, 283, 147, 67, 29, 9, 3

Offset

15,1

Comments

In Spanish dominoes (double sixes) each of the four players gets a hand of seven stones. a(n) represents the number of possible different hands of n points. The lowest possible number of points in a hand is 15: (0-0 / 0-1 / 1-1 / 0-2 / 1-2 / 0-3) and one of the following stones: (2-2 / 1-3 / 0-4) which is three different combinations.

The highest hand is 69 points (6-6 / 6-5 / 5-5 / 6-4 / 5-4 / 6-3) and any of: (4-4 / 5-3 / 6-2). The sequence is finite and symmetrical around the peak: a(42) = 65746.

The sum of a(15) through a(69) is C(28,7) = 1184040.

Links

Table of n, a(n) for n=15..69.

Wikipedia, Dominoes, Tiles and suits

Formula

a(42+n) = a(42-n).

Example

a(15)=3 since there are only 3 combinations of 7 stones that yield a hand of 15 points.

Mathematica

Last /@ Tally[ Sort[ Total /@ Flatten /@ Subsets[ Flatten[ Table[{i, j} - 1, {i, 7}, {j, i}], 1], {7}]]] (* Giovanni Resta, Jun 23 2015 *)

Crossrefs

Sequence in context: A047137 A058145 A218915 * A161590 A192245 A338645

Adjacent sequences: A258061 A258062 A258063 * A258065 A258066 A258067

Keyword

full,fini,nonn

Author

Sergio Pimentel, May 18 2015

Status

approved