cp's OEIS Frontend

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.

%I A152568 #11 Jan 10 2019 02:19:16
%S A152568 -1,1,-1,2,-1,-1,4,-2,-1,-1,8,-4,-2,-1,-1,16,-8,-4,-2,-1,-1,32,-16,-8,
%T A152568 -4,-2,-1,-1,64,-32,-16,-8,-4,-2,-1,-1,128,-64,-32,-16,-8,-4,-2,-1,-1,
%U A152568 256,-128,-64,-32,-16,-8,-4,-2,-1,-1,512,-256,-128,-64,-32,-16,-8,-4,-2
%N 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.
%C A152568 Except for n = 0, the row sums are zero.
%F A152568 From _Franck Maminirina Ramaharo_, Jan 08 2019: (Start)
%F A152568 G.f.: -(1 - 3*y + 2*x*y^2)/(1 - (2 + x)*y + 2*x*y^2).
%F A152568 E.g.f.: (exp(2*y) - exp(x*y))*(1 - x)/(2 - x) - 1. (End)
%e A152568 Triangle begins:
%e A152568    -1;
%e A152568     1,   -1;
%e A152568     2,   -1,   -1;
%e A152568     4,   -2,   -1,  -1;
%e A152568     8,   -4,   -2,  -1,  -1;
%e A152568    16,   -8,   -4,  -2,  -1,  -1;
%e A152568    32,  -16,   -8,  -4,  -2,  -1, -1;
%e A152568    64,  -32,  -16,  -8,  -4,  -2, -1, -1;
%e A152568   128,  -64,  -32, -16,  -8,  -4, -2, -1, -1;
%e A152568   256, -128,  -64, -32, -16,  -8, -4, -2, -1, -1;
%e A152568   512, -256, -128, -64, -32, -16, -8, -4, -2, -1, -1;
%e A152568   ...
%t A152568 b[0] = {-1}; b[1] = {1, -1};
%t A152568 b[n_] := b[n] = Join[{2^(n - 1)}, {-b[n - 1][[1]]}, Table[b[n - 1][[i]], {i, 2, Length[b[n - 1]]}]]
%t A152568 Flatten[Table[b[n], {n, 0, 10}]]
%o A152568 (Maxima)
%o A152568 T(n, k) := if k = n then -1 else if k = 0 then 2^(n - 1) else -2^(n - k - 1)$
%o A152568 create_list(T(n, k), n, 0, 20, k, 0, n); /* _Franck Maminirina Ramaharo_, Jan 08 2019 */
%Y A152568 Cf. A057728, A152570, A152571, A152572.
%K A152568 sign,tabl,easy
%O A152568 0,4
%A A152568 _Roger L. Bagula_, Dec 08 2008
%E A152568 Unrelated material removed by the Assoc. Eds. of the OEIS, Jun 07 2010