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A187034
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Number triangle T(n,k) = (-1)^(n-k) if binomial(k, n-k) > 0, 0 otherwise, with 0 <= k <= n.
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4
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1, 0, 1, 0, -1, 1, 0, 0, -1, 1, 0, 0, 1, -1, 1, 0, 0, 0, 1, -1, 1, 0, 0, 0, -1, 1, -1, 1, 0, 0, 0, 0, -1, 1, -1, 1, 0, 0, 0, 0, 1, -1, 1, -1, 1, 0, 0, 0, 0, 0, 1, -1, 1, -1, 1, 0, 0, 0, 0, 0, -1, 1, -1, 1, -1, 1, 0, 0, 0, 0, 0, 0, -1, 1, -1, 1, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, 1
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OFFSET
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0
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COMMENTS
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Alternating sign version of A101688. A187036 is an eigensequence. Diagonal sums are A187035. Row sums are A133872.
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LINKS
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Table of n, a(n) for n=0..86.
Boris Putievskiy, Transformations (of) Integer Sequences And Pairing Functions, 2012, arXiv:1212.2732 [math.CO].
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FORMULA
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From Boris Putievskiy, Jan 09 2013: (Start)
a(n) = A101688(n)*(-1)^(A003056(n) + A002260(n) + 1).
a(n) = floor((2*A002260(n)+1)/(A003056(n)+3))*(-1)^(A003056(n) + A002260(n) + 1).
a(n) = floor((2*n-t*(t+1)+1)/(t+3))*(-1)^(n-t*(t-1)/2+1), n > 0, where t = floor((-1+sqrt(8*n-7))/2). (End)
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EXAMPLE
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Triangle begins
1;
0, 1;
0, -1, 1;
0, 0, -1, 1;
0, 0, 1, -1, 1;
0, 0, 0, 1, -1, 1;
0, 0, 0, -1, 1, -1, 1;
0, 0, 0, 0, -1, 1, -1, 1;
0, 0, 0, 0, 1, -1, 1, -1, 1;
0, 0, 0, 0, 0, 1, -1, 1, -1, 1;
0, 0, 0, 0, 0, -1, 1, -1, 1, -1, 1;
0, 0, 0, 0, 0, 0, -1, 1, -1, 1, -1, 1;
0, 0, 0, 0, 0, 0, 1, -1, 1, -1, 1, -1, 1;
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MATHEMATICA
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T[n_, k_] := Boole[n <= 2k] (-1)^(n-k);
Table[T[n, k], {n, 0, 12}, {k, 0, n}] // Flatten (* Jean-François Alcover, Oct 05 2018 *)
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PROG
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(PARI) T(n, k)=if(n<=2*k, (-1)^(n-k), 0) \\ Charles R Greathouse IV, Dec 28 2011
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CROSSREFS
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Sequence in context: A127241 A087748 A117446 * A101688 A155031 A155029
Adjacent sequences: A187031 A187032 A187033 * A187035 A187036 A187037
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KEYWORD
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sign,tabl,easy
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AUTHOR
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Paul Barry, Mar 08 2011
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STATUS
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approved
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