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 A152571 Triangle T(n,k) read by rows: T(n,n) = -1, T(n,0) = 4^(n - 1), T(n,k) = -4^(n - k - 1), 1 <= k <= n - 1. 4

%I

%S -1,1,-1,4,-1,-1,16,-4,-1,-1,64,-16,-4,-1,-1,256,-64,-16,-4,-1,-1,

%T 1024,-256,-64,-16,-4,-1,-1,4096,-1024,-256,-64,-16,-4,-1,-1,16384,

%U -4096,-1024,-256,-64,-16,-4,-1,-1,65536,-16384,-4096,-1024,-256,-64,-16,-4,-1,-1

%N Triangle T(n,k) read by rows: T(n,n) = -1, T(n,0) = 4^(n - 1), T(n,k) = -4^(n - k - 1), 1 <= k <= n - 1.

%F From _Franck Maminirina Ramaharo_, Jan 08 2019: (Start)

%F G.f.: -(1 - 5*y + 2*x*y^2)/(1 - (4 + x)*y + 4*x*y^2).

%F E.g.f.: -(4 - x - (2 - x)*exp(4*y) + (6 - 2*x)*exp(x*y))/(8 - 2*x). (End)

%e Triangle begins:

%e -1;

%e 1, -1;

%e 4, -1, -1;

%e 16, -4, -1, -1;

%e 64, -16, -4, -1, -1;

%e 256, -64, -16, -4, -1, -1;

%e 1024, -256, -64, -16, -4, -1, -1;

%e 4096, -1024, -256, -64, -16, -4, -1, -1;

%e 16384, -4096, -1024, -256, -64, -16, -4, -1, -1;

%e 65536, -16384, -4096, -1024, -256, -64, -16, -4, -1, -1;

%e 262144, -65536, -16384, -4096, -1024, -256, -64, -16, -4, -1, -1;

%e ...

%t b[0] = {-1}; b[1] = {1, -1};

%t b[n_] := b[n] = Join[{4^(n - 1)}, {-b[n - 1][[1]]}, Table[b[n - 1][[i]], {i, 2, Length[b[n - 1]]}]];

%t Flatten[Table[b[n], {n, 0, 10}]]

%o (Maxima)

%o T(n, k) := if k = n then -1 else if k = 0 then 4^(n - 1) else -4^(n - k - 1)\$

%o create_list(T(n, k), n, 0, 20, k, 0, n); /* _Franck Maminirina Ramaharo_, Jan 08 2019 */

%Y Row sums (except row 0): A020988.

%Y Cf. A057728, A152568, A152570, A152572.

%K sign,easy,tabl

%O 0,4

%A _Roger L. Bagula_, Dec 08 2008

%E Edited by _Franck Maminirina Ramaharo_, Jan 08 2019

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Last modified May 28 21:37 EDT 2020. Contains 334690 sequences. (Running on oeis4.)