A152568 - OEIS

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.

-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

Table of n, a(n) for n=0..63.

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