A111967 Inverse of number triangle A101688.

1, 0, 1, 0, -1, 1, 0, 1, -1, 1, 0, 0, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, 0, 0, 0, 0, -1, 1, 0, 1, -1, 1, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, -1, 1, 0, -1, 1, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1

Offset: 0

Author

Paul Barry, Aug 23 2005

Keywords

• sign
• tabl

Comments

Row sums are the Fredholm-Rueppel sequence A036987 [conjecture].

Examples

			Triangle begins
1,
0, 1,
0, -1, 1,
0, 1, -1, 1,
0, 0, 0, -1, 1,
0, -1, 1, 0, -1, 1,
0, 0, 0, 0, 0, -1, 1,
0, 1, -1, 1, 0, 0, -1, 1,
0, 0, 0, 0, 0, 0, 0, -1, 1,
0, 0, 0, -1, 1, 0, 0, 0, -1, 1,
0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1,
0, -1, 1, 0, -1, 1, 0, 0, 0, 0, -1, 1,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1,
0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, -1, 1,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1,
0, 1, -1, 1, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, -1, 1,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1
		

Links

• R. J. Mathar, OEIS A111967

Crossrefs

Cf. A036987, A101688

Programs

PARI

T(n, k) = if(binomial(k, n-k)>0, 1, 0); \\ A101688
mrepeat(nn) = matrix(nn, nn, n, k, T(n-1, k-1)); \\ A101688
lista(nn) = my(m=mrepeat(nn+1), im = 1/m, list = List()); for (n = 1, nn, listput(list, vector(n, k, im[n,k]));); Vec(list); \\ Michel Marcus, Nov 12 2022

Formula

G.f. of k-th column is x^k*if(k=0,1,x*Sum_{j>=0} (-1)^j*x^(-2^(j/2)*(((k+2)/(2*sqrt(2))-(k+1))(-1)^j-(k+2)/(2*sqrt(2))-(k+1))-(k+2))+1-x). - Paul Barry, Jan 30 2007