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A152570
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Triangle T(n,k) read by rows: T(n,n) = -1, T(n,0) = 3^(n - 1), T(n,k) = -3^(n - k - 1), 1 <= k <= n - 1.
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3
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-1, 1, -1, 3, -1, -1, 9, -3, -1, -1, 27, -9, -3, -1, -1, 81, -27, -9, -3, -1, -1, 243, -81, -27, -9, -3, -1, -1, 729, -243, -81, -27, -9, -3, -1, -1, 2187, -729, -243, -81, -27, -9, -3, -1, -1, 6561, -2187, -729, -243, -81, -27, -9, -3, -1, -1, 19683, -6561, -2187
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table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,4
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LINKS
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FORMULA
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G.f.: -(1 - 4*y + 2*x*y^2)/(1 - (3 + x)*y + 3*x*y^2).
E.g.f.: -(6 - 2*x - (3 - 2*x)*exp(3*y) + (6 - 3*x)*exp(x*y))/(9 - 3*x). (End)
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EXAMPLE
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Triangle begins:
-1;
1, -1;
3, -1, -1;
9, -3, -1, -1;
27, -9, -3, -1, -1;
81, -27, -9, -3, -1, -1;
243, -81, -27, -9, -3, -1, -1;
729, -243, -81, -27, -9, -3, -1, -1;
2187, -729, -243, -81, -27, -9, -3, -1, -1;
6561, -2187, -729, -243, -81, -27, -9, -3, -1, -1;
19683, -6561, -2187, -729, -243, -81, -27, -9, -3, -1, -1;
...
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MATHEMATICA
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b[0] = {-1}; b[1] = {1, -1};
b[n_] := b[n] = Join[{3^(n - 1)}, {-b[n - 1][[1]]}, Table[b[n - 1][[i]], {i, 2, Length[b[n - 1]]}]];
Flatten[Table[b[n], {n, 0, 10}]]
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PROG
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(Maxima)
T(n, k) := if k = n then -1 else if k = 0 then 3^(n - 1) else -3^(n - k - 1)$
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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