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A258064
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Number of hands of n points in Spanish dominoes.
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0
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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
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OFFSET
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15,1
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COMMENTS
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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.
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LINKS
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FORMULA
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a(42+n) = a(42-n).
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EXAMPLE
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a(15)=3 since there are only 3 combinations of 7 stones that yield a hand of 15 points.
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MATHEMATICA
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Last /@ Tally[ Sort[ Total /@ Flatten /@ Subsets[ Flatten[ Table[{i, j} - 1, {i, 7}, {j, i}], 1], {7}]]] (* Giovanni Resta, Jun 23 2015 *)
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CROSSREFS
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KEYWORD
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full,fini,nonn
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AUTHOR
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STATUS
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approved
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