A107416 Triangle, read by rows: T(0,0) = 1, T(n,k) = F(n+1)*T(n-1,k) - T(n-1,k-1) where F(n+1) is the (n+1)st Fibonacci number.

1, 1, -1, 2, -3, 1, 6, -11, 6, -1, 30, -61, 41, -11, 1, 240, -518, 389, -129, 19, -1, 3120, -6974, 5575, -2066, 376, -32, 1, 65520, -149574, 124049, -48961, 9962, -1048, 53, -1, 2227680, -5151036, 4367240, -1788723, 387669, -45594, 2850, -87, 1

Offset

0,4

Comments

For n>0, the row sums are 0. For n>1, sum(k=0..n) 2^k*T(n,k) = 0. The first subdiagonal (1,-3,6,-11,19,...) is an alternating signed version of A001911 (Fibonacci numbers - 2). The first row is A003266 (product of Fibonacci numbers).

Links

Table of n, a(n) for n=0..44.

Example

Triangle begins
1;
1, -1;
2, -3, 1;
6, -11, 6, -1;

Crossrefs

Sequence in context: A174893 A008275 A130534 * A105613 A334951 A263634

Adjacent sequences: A107413 A107414 A107415 * A107417 A107418 A107419

Keyword

sign,tabl

Author

Gerald McGarvey, May 26 2005

Extensions

Corrected a sign in the definition. - N. J. A. Sloane, Apr 11 2013

Status

approved