A187034 Number triangle T(n,k) = (-1)^(n-k) if binomial(k, n-k) > 0, 0 otherwise, with 0 <= k <= n.

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

Offset

0

Comments

Alternating sign version of A101688. A187036 is an eigensequence. Diagonal sums are A187035. Row sums are A133872.

Links

Table of n, a(n) for n=0..86.

Boris Putievskiy, Transformations (of) Integer Sequences And Pairing Functions, 2012, arXiv:1212.2732 [math.CO], 2012.

Formula

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)

Example

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;

Mathematica

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 *)

Prog

(PARI) T(n, k)=if(n<=2*k, (-1)^(n-k), 0) \\ Charles R Greathouse IV, Dec 28 2011

Crossrefs

Sequence in context: A127241 A087748 A117446 * A101688 A155029 A155031

Adjacent sequences: A187031 A187032 A187033 * A187035 A187036 A187037

Keyword

sign,tabl,easy

Author

Paul Barry, Mar 08 2011

Status

approved