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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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Except for n = 0, the row sums are zero. LINKS 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 Cf. A057728, A152570, A152571, A152572. Sequence in context: A140997 A140996 A141020 * A155038 A057728 A176463 Adjacent sequences:  A152565 A152566 A152567 * A152569 A152570 A152571 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

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Last modified December 15 09:05 EST 2019. Contains 329995 sequences. (Running on oeis4.)