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A178535
Matrix inverse of A178534.
3
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
1,2
COMMENTS
Except for first term row sums equal a signed version of A023022.
EXAMPLE
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
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 *)
CROSSREFS
Cf. First column is A178536.
Sequence in context: A050372 A037802 A037879 * A025449 A047988 A037818
KEYWORD
sign,tabl
AUTHOR
Mats Granvik, May 29 2010
STATUS
approved