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Search: id:A122837
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| A122837 |
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Triangle T(n,k), 0<=k<=n, defined by : T(n,k)=0 if k<0, T(n,k)=0 if k>n,T(0,0)=1, T(1,0)=1, T(1,1)=-1, T(n,k)=T(n-1,k-1)+T(n-1,k)+T(n-2,k). |
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+0
1
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| 1, 1, -1, 2, 0, -1, 3, 1, -1, -1, 5, 4, -1, -2, -1, 8, 10, 2, -4, -3, -1, 13, 22, 11, -4, -8, -4, -1, 21, 45, 35, 3, -15, -13, -5, -1, 34, 88, 91, 34, -20, -32, -19, -6, -1, 55, 167, 214, 128, -1, -65, -56, -26, -7, -1
(list; table; graph; listen)
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OFFSET
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0,4
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FORMULA
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Sum{k,0<=k<=n}T(n,k)=A000129(n-1)for n>0 .T(n,0) = Fibonacci(n+1)=A000045(n+1).
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EXAMPLE
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Triangle begins:
1;
1, -1;
2, 0, -1;
3, 1, -1, -1;
5, 4, -1, -2, -1;
8, 10, 2, -4, -3, -1;
13, 22, 11, -4, -8, -4, -1;
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CROSSREFS
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Sequence in context: A065432 A094184 A078805 this_sequence A130504 A044942 A114912
Adjacent sequences: A122834 A122835 A122836 this_sequence A122838 A122839 A122840
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KEYWORD
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sign,tabl
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AUTHOR
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Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 23 2006
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