A110515 Sequence array for (1 - x + x^2 + x^3)/(1 - x^4).

1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1

Offset: 0

Author

Paul Barry, Jul 24 2005

Keywords

• easy
• sign
• tabl

Comments

Row sums are A106249. Diagonal sums are A110514.

Examples

			Rows begin
   1;
  -1,  1;
   1, -1,  1;
   1,  1, -1,  1;
   1,  1,  1, -1,  1;
  -1,  1,  1,  1, -1,  1;
   1, -1,  1,  1,  1,- 1,  1;
		

Links

• G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

Programs

Mathematica

Table[If[k <= n, -Sin[Pi*(n - k)/2] + Cos[Pi*(n - k)]/2 + 1/2, 0], {n,0, 10}, {k, 0, n}]//Flatten (* G. C. Greubel, Aug 29 2017 *)

PARI

for(n=0,20, for(k=0,n, print1(round(if(k<=n, -sin(Pi*(n-k)/2) + cos(Pi*(n-k))/2 + 1/2, 0)), ", "))) \\ G. C. Greubel, Aug 29 2017

Formula

Riordan array ((1 - x + x^2 + x^3)/(1 - x^4), 1).

Column k has g.f. x^k*(1 - x + x^2 + x^3)/(1 - x^4).

T(n, k) = if(k <= n, -sin(Pi*(n-k)/2) + cos(Pi*(n-k))/2 + 1/2, 0).

T(n, k) = if(k <= n, Jacobi(2^(n-k), 2(n-k)+1), 0) [conjecture].