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%I #10 Jun 23 2015 18:59:17
%S 3,9,29,67,147,283,526,893,1470,2287,3451,4990,7030,9559,12697,16375,
%T 20664,25406,30621,36034,41618,47022,52174,56696,60548,63362,65186,
%U 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
%N Number of hands of n points in Spanish dominoes.
%C 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.
%C 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.
%C The sum of a(15) through a(69) is C(28,7) = 1184040.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Dominoes#Tiles_and_suits">Dominoes, Tiles and suits</a>
%F a(42+n) = a(42-n).
%e a(15)=3 since there are only 3 combinations of 7 stones that yield a hand of 15 points.
%t Last /@ Tally[ Sort[ Total /@ Flatten /@ Subsets[ Flatten[ Table[{i, j} - 1, {i, 7}, {j, i}], 1], {7}]]] (* _Giovanni Resta_, Jun 23 2015 *)
%K full,fini,nonn
%O 15,1
%A _Sergio Pimentel_, May 18 2015
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