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A086329
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Triangle T(n,k) read by rows, given by [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, ...] DELTA [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, ...] where DELTA is the operator defined in A084938.
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3
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1, 0, 1, 0, 1, 1, 0, 1, 4, 1, 0, 1, 9, 11, 1, 0, 1, 16, 48, 26, 1, 0, 1, 25, 140, 202, 57, 1, 0, 1, 36, 325, 916, 747, 120, 1, 0, 1, 49, 651, 3045, 5071, 2559, 247, 1, 0, 1, 64, 1176, 8260, 23480, 25300, 8362, 502, 1, 0, 1, 81, 1968, 19404, 84456, 159736, 117962, 26520
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OFFSET
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0,9
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COMMENTS
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See A087903 for another version (transposed). - Philippe Deléham, Jun 13 2004
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LINKS
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Table of n, a(n) for n=0..63.
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FORMULA
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Sum(0<=k<=n, T(n, k))= A086211(n, 0). T(n, 1)= 1; n>0. T(n, 2)= (n-1)^2; n>0. T(k+1, k)= 2^(k+1)-k-2 = A000295(k+1).
Sum{k = 0..n} T(n, k) = A074664(n+1) . - Philippe Deléham, Jun 13 2004
Sum_{k, 0<=k<=n} T(n,k)*2^k = A171151(n). [From Philippe DELEHAM, Dec 05 2009]
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EXAMPLE
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Triangle begins:
1;
0, 1;
0, 1, 1;
0, 1, 4, 1;
0, 1, 9, 11, 1;
0, 1, 16, 48, 26, 1;
0, 1, 25, 140, 202, 57, 1;
0, 1, 36, 325, 916, 747, 120, 1;
0, 1, 49, 651, 3045, 5071, 2559, 247, 1;
0, 1, 64, 1176, 8260, 23480, 25300, 8362, 502, 1 ;...
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CROSSREFS
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Cf. A000290 A000295 A086211.
Sequence in context: A035588 A073027 A099793 * A085852 A123125 A173018
Adjacent sequences: A086326 A086327 A086328 * A086330 A086331 A086332
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Philippe Deléham, Aug 30 2003, Jun 12 2007
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STATUS
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approved
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