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A166322
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The number of times a point sum n is attained in all 7^6 permutations of throwing 7 dice.
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2
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1, 7, 28, 84, 210, 462, 917, 1667, 2807, 4417, 6538, 9142, 12117, 15267, 18327, 20993, 22967, 24017, 24017, 22967, 20993, 18327, 15267, 12117, 9142, 6538, 4417, 2807, 1667, 917, 462, 210, 84, 28, 7, 1
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OFFSET
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7,2
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COMMENTS
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The sum for any number of dice can be obtained by summing the trailing six terms of the sequence above - assuming leading zeros.
1 1 1 1 1 1
1 2 3 4 5 6 5 4 3 2 1
1 3 6 10 15 21 25 27 27 25 21 15 10 6 3 1
1 4 10 20 35 56 80 104 125 140 125 104 80 56 35 20 10 4 1
etc.
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LINKS
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Table of n, a(n) for n=7..42.
Dice
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FORMULA
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F_{s,i}(k)= sum(n=0, floor((k-i)/s), (-1)^n*binomial(n,i)*binomial(i-1,k-s*n-1)).
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PROG
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(PARI) Vec(((sum(k=1, 6, x^k))^7+O(x^66))) /* Joerg Arndt, Mar 04 2013 */
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CROSSREFS
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A056150 gives sums for 3 dice.
A108907 gives sums for 6 dice.
A063260 gives the sums for 2 dice through to 6 dice.
Sequence in context: A163705 A162595 A073363 * A008499 A049018 A008489
Adjacent sequences: A166319 A166320 A166321 * A166323 A166324 A166325
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KEYWORD
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nonn,fini,full
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AUTHOR
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Robert Goodhand (robert(AT)rgoodhand.fsnet.co.uk), Oct 11 2009
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STATUS
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approved
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