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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
-1, 1, -1, 4, -1, -1, 16, -4, -1, -1, 64, -16, -4, -1, -1, 256, -64, -16, -4, -1, -1, 1024, -256, -64, -16, -4, -1, -1, 4096, -1024, -256, -64, -16, -4, -1, -1, 16384, -4096, -1024, -256, -64, -16, -4, -1, -1, 65536, -16384, -4096, -1024, -256, -64, -16, -4, -1, -1
OFFSET
0,4
FORMULA
From Franck Maminirina Ramaharo, Jan 08 2019: (Start)
G.f.: -(1 - 5*y + 2*x*y^2)/(1 - (4 + x)*y + 4*x*y^2).
E.g.f.: -(4 - x - (2 - x)*exp(4*y) + (6 - 2*x)*exp(x*y))/(8 - 2*x). (End)
EXAMPLE
Triangle begins:
-1;
1, -1;
4, -1, -1;
16, -4, -1, -1;
64, -16, -4, -1, -1;
256, -64, -16, -4, -1, -1;
1024, -256, -64, -16, -4, -1, -1;
4096, -1024, -256, -64, -16, -4, -1, -1;
16384, -4096, -1024, -256, -64, -16, -4, -1, -1;
65536, -16384, -4096, -1024, -256, -64, -16, -4, -1, -1;
262144, -65536, -16384, -4096, -1024, -256, -64, -16, -4, -1, -1;
...
MATHEMATICA
b[0] = {-1}; b[1] = {1, -1};
b[n_] := b[n] = Join[{4^(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 4^(n - 1) else -4^(n - k - 1)$
create_list(T(n, k), n, 0, 20, k, 0, n); /* Franck Maminirina Ramaharo, Jan 08 2019 */
CROSSREFS
Row sums (except row 0): A020988.
Sequence in context: A116469 A156599 A010320 * A008304 A203846 A118185
KEYWORD
sign,easy,tabl
AUTHOR
Roger L. Bagula, Dec 08 2008
EXTENSIONS
Edited by Franck Maminirina Ramaharo, Jan 08 2019
STATUS
approved