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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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..54.

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.

Cf. A057728, A152568, A152570, A152572.

Sequence in context: A116469 A156599 A010320 * A008304 A203846 A118185

Adjacent sequences:  A152568 A152569 A152570 * A152572 A152573 A152574

KEYWORD

sign,easy,tabl

AUTHOR

Roger L. Bagula, Dec 08 2008

EXTENSIONS

Edited by Franck Maminirina Ramaharo, Jan 08 2019

STATUS

approved

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Last modified December 8 14:18 EST 2021. Contains 349596 sequences. (Running on oeis4.)