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Search: id:A061676
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| A061676 |
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Triangle T(n,k) of number of ways of throwing k standard dice to produce a total of n. |
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+0
3
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| 1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 6, 4, 1, 1, 5, 10, 10, 5, 1, 0, 6, 15, 20, 15, 6, 1, 0, 5, 21, 35, 35, 21, 7, 1, 0, 4, 25, 56, 70, 56, 28, 8, 1, 0, 3, 27, 80, 126, 126, 84, 36, 9, 1, 0, 2, 27, 104, 205, 252, 210, 120, 45, 10, 1, 0, 1, 25, 125, 305, 456, 462, 330, 165, 55, 11, 1
(list; table; graph; listen)
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OFFSET
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1,5
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FORMULA
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T(n, k)=T(n-1, k-1)+T(n-2, k-1)+T(n-3, k-1)+T(n-4, k-1)+T(n-5, k-1)+T(n-6, k-1) starting with T(0, 0)=1. T(n, k)=T(7k-n, k); if n>6k or n<k, T(n, k)=0; if n<k+6, T(n, k)=C(n-1, k-1); if n>6k-6, T(n, k)=C(7k-n-1, k-1); T([7k/2], k)=A018901(k).
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EXAMPLE
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Rows start: 1; 1,1; 1,2,1; 1,3,3,1; 1,4,6,4,1; 1,5,10,10,5,1; 0,6,15,20,15,6,1; 0,5,21,35,35,21,7,1; etc. T(8,2)=5 since 8 =2+6 =3+5 =4+4 =5+3 =6+2.
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CROSSREFS
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First 21 terms as A007318 (see formula). Cf. A001592, A069713.
Sequence in context: A034930 A095142 A089239 this_sequence A095145 A095144 A034932
Adjacent sequences: A061673 A061674 A061675 this_sequence A061677 A061678 A061679
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KEYWORD
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nonn,tabl
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Apr 01 2002
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