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Search: id:A077227
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| A077227 |
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Triangle of compositions of n into exactly k parts each no more than k. |
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+0
3
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| 1, 0, 1, 0, 2, 1, 0, 1, 3, 1, 0, 0, 6, 4, 1, 0, 0, 7, 10, 5, 1, 0, 0, 6, 20, 15, 6, 1, 0, 0, 3, 31, 35, 21, 7, 1, 0, 0, 1, 40, 70, 56, 28, 8, 1, 0, 0, 0, 44, 121, 126, 84, 36, 9, 1, 0, 0, 0, 40, 185, 252, 210, 120, 45, 10, 1, 0, 0, 0, 31, 255, 456, 462, 330, 165, 55, 11, 1, 0, 0, 0, 20
(list; table; graph; listen)
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OFFSET
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1,5
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LINKS
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Index entries for sequences related to compositions
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FORMULA
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T(n, k) =A077228(n, k)-A077228(n-1, k). If n>=k^2, T(n, k)=0. If k<=n<2k, T(n, k)=C(n-1, k-1).
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EXAMPLE
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Rows start: 1; 0,1; 0,2,1; 0,1,3,1; 0,0,6,4,1; 0,0,7,10,5,1; etc. Columns start: 1,0,0,0,...; 1,2,1,0,0,0,...; 1,3,6,7,6,3,1,0,0,0,...; 1,4,10,20,31,40,44,40,31,20,10,4,1,0,0,0,...; etc. T(6,3)=7 since 6 can be written as 1+2+3, 1+3+2, 2+1+3, 2+2+2, 2+3+1, 3+1+2, or 3+2+1.
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CROSSREFS
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Column sums are A000312. Row sums are A077229. Central diagonal is A000984 offset. Right hand side is right hand side of A007318. Cf. A077228.
Sequence in context: A131185 A052249 A030528 this_sequence A089263 A156135 A047265
Adjacent sequences: A077224 A077225 A077226 this_sequence A077228 A077229 A077230
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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), Oct 29 2002
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