OFFSET
0,4
FORMULA
From Franck Maminirina Ramaharo, Jan 08 2019: (Start)
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)
EXAMPLE
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;
...
MATHEMATICA
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}]]
PROG
(Maxima)
T(n, k) := if k = n then -1 else if k = 0 then 3^(n - 1) else -3^(n - k - 1)$
create_list(T(n, k), n, 0, 20, k, 0, n); /* Franck Maminirina Ramaharo, Jan 08 2019 */
CROSSREFS
KEYWORD
AUTHOR
Roger L. Bagula, Dec 08 2008
EXTENSIONS
Edited by Franck Maminirina Ramaharo, Jan 08 2019
STATUS
approved