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A152568
Triangle T(n,k) read by rows: T(n,n) = -1, T(n,0) = 2^(n - 1), T(n,k) = -2^(n - k - 1), 1 <= k <= n - 1.
6
-1, 1, -1, 2, -1, -1, 4, -2, -1, -1, 8, -4, -2, -1, -1, 16, -8, -4, -2, -1, -1, 32, -16, -8, -4, -2, -1, -1, 64, -32, -16, -8, -4, -2, -1, -1, 128, -64, -32, -16, -8, -4, -2, -1, -1, 256, -128, -64, -32, -16, -8, -4, -2, -1, -1, 512, -256, -128, -64, -32, -16, -8, -4, -2
OFFSET
0,4
COMMENTS
Except for n = 0, the row sums are zero.
FORMULA
From Franck Maminirina Ramaharo, Jan 08 2019: (Start)
G.f.: -(1 - 3*y + 2*x*y^2)/(1 - (2 + x)*y + 2*x*y^2).
E.g.f.: (exp(2*y) - exp(x*y))*(1 - x)/(2 - x) - 1. (End)
EXAMPLE
Triangle begins:
-1;
1, -1;
2, -1, -1;
4, -2, -1, -1;
8, -4, -2, -1, -1;
16, -8, -4, -2, -1, -1;
32, -16, -8, -4, -2, -1, -1;
64, -32, -16, -8, -4, -2, -1, -1;
128, -64, -32, -16, -8, -4, -2, -1, -1;
256, -128, -64, -32, -16, -8, -4, -2, -1, -1;
512, -256, -128, -64, -32, -16, -8, -4, -2, -1, -1;
...
MATHEMATICA
b[0] = {-1}; b[1] = {1, -1};
b[n_] := b[n] = Join[{2^(n - 1)}, {-b[n - 1][[1]]}, Table[b[n - 1][[i]], {i, 2, Length[b[n - 1]]}]]
Flatten[Table[b[n], {n, 0, 10}]]
PROG
(Maxima)
T(n, k) := if k = n then -1 else if k = 0 then 2^(n - 1) else -2^(n - k - 1)$
create_list(T(n, k), n, 0, 20, k, 0, n); /* Franck Maminirina Ramaharo, Jan 08 2019 */
CROSSREFS
KEYWORD
sign,tabl,easy
AUTHOR
Roger L. Bagula, Dec 08 2008
EXTENSIONS
Unrelated material removed by the Assoc. Eds. of the OEIS, Jun 07 2010
STATUS
approved