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A123149
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Triangle T(n,k), 0<=k<=n, read by rows given by [1, 0, -1, 0, 0, 0, 0, 0, ...] DELTA [0, 1, 0, -1, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938.
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1
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1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 2, 2, 1, 0, 1, 2, 3, 2, 1, 0, 1, 3, 5, 5, 3, 1, 0, 1, 3, 6, 7, 6, 3, 1, 0, 1, 4, 9, 13, 13, 9, 4, 1, 0, 1, 4, 10, 16, 19, 16, 10, 4, 1, 0, 1, 5, 14, 26, 35, 35, 26, 14, 5, 1, 0, 1, 5, 15, 30, 45, 51, 45, 30, 15, 5, 1, 0, 1, 6, 20, 45, 75, 96, 96, 75, 45, 20, 6, 1, 0, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,12
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FORMULA
| T(n,k)=T(n,n-1-k) . Sum_{k, 0<=k<=n}T(n,k)=A038754(n-1), for n>=1 . T(2*n,n)=A005773(n) . T(2*n+1,n)=A002426(n) . T(n,k)=T(n-1,k-1)+T(n-1,k)if n even, T(n,k)=T(n-1,k-1)+T(n-2,k)if n odd, T(0,0)=1, T(1,0)=1, T(1,1)=0, T(n,k)=0 if k<0 or if k>n.
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EXAMPLE
| Triangle begins:
1;
1, 0;
1, 1, 0;
1, 1, 1, 0;
1, 2, 2, 1, 0;
1, 2, 3, 2, 1, 0;
1, 3, 5, 5, 3, 1, 0;
1, 3, 6, 7, 6, 3, 1, 0;
1, 4, 9, 13, 13, 9, 4, 1, 0;
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CROSSREFS
| Cf. A027907.
Sequence in context: A194527 A104244 A116403 * A185158 A185700 A061926
Adjacent sequences: A123146 A123147 A123148 * A123150 A123151 A123152
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KEYWORD
| nonn,tabl
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AUTHOR
| Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 05 2006
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