A178535 Matrix inverse of A178534.

1, -2, 1, -1, -1, 1, 0, -1, -1, 1, -1, -1, 0, -1, 1, 1, 0, -2, 0, -1, 1, -1, -1, 0, -1, 0, -1, 1, 0, 0, 0, -1, -1, 0, -1, 1, 0, 0, -1, -1, 0, -1, 0, -1, 1, 1, 0, -1, 1, -2, 0, -1, 0, -1, 1, -1, -1, 0, -1, 0, -1, 0, -1, 0, -1, 1, 0, 1, 1, -1, 0, -1, -1, 0, -1, 0, -1, 1, -1, -1, 0, -1, 0, -1, 0, -1, 0, -1, 0, -1, 1

Offset: 1

Author

Mats Granvik, May 29 2010

Keywords

• sign
• tabl

Comments

Except for first term row sums equal a signed version of A023022.

Examples

			Table begins:
   1
  -2  1
  -1 -1  1
   0 -1 -1  1
  -1 -1  0 -1  1
   1  0 -2  0 -1  1
  -1 -1  0 -1  0 -1  1
   0  0  0 -1 -1  0 -1  1
   0  0 -1 -1  0 -1  0 -1  1
   1  0 -1  1 -2  0 -1  0 -1  1
  -1 -1  0 -1  0 -1  0 -1  0 -1  1
		

Crossrefs

Cf. First column is A178536.

Programs

Maple

A178535 := proc(n, l)
    option remember;
    a := 0 ;
    if n = l then
        a := 1 ;
    end if;
    for k from l to n-1 do
        a := a-A178534(n, k)*procname(k, l) ;
    end do:
    a/A178534(n, n) ;
end proc:
seq(seq(A178535(n,k),k=1..n),n=1..12) ; # R. J. Mathar, Oct 28 2010

Mathematica

nmax = 13;
(* T is A178534 *)
T[n_, 1] := Fibonacci[n+1];
T[n_, k_] := T[n, k] = If[k > n, 0, Sum[T[n-i, k-1], {i, 1, k-1}] - Sum[T[n-i, k], {i, 1, k-1}]];
A178535 = Inverse[Array[T, {nmax, nmax}]];
Table[A178535[[n, k]], {n, 1, nmax}, {k, 1, n}] // Flatten (* Jean-François Alcover, Feb 23 2024 *)