A143439 Triangle whose n-th row is the expansion of x*(x^n*(x - 1) + (-1)^n*2).

-1, -1, 0, 1, 1, 0, -2, -1, 1, 0, 2, 0, -1, 1, 0, -2, 0, 0, -1, 1, 0, 2, 0, 0, 0, -1, 1, 0, -2, 0, 0, 0, 0, -1, 1, 0, 2, 0, 0, 0, 0, 0, -1, 1, 0, -2, 0, 0, 0, 0, 0, 0, -1, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1

Offset

-1,7

Links

Table of n, a(n) for n=-1..88.

Eriko Hironaka, Salem-Boyd sequences and Hopf plumbing, Osaka J. Math. Volume 43, Number 3 (2006), 497-516.

Eriko Hironaka, Salem-Boyd sequences and Hopf plumbing, arXiv:math/0506602 [math.GT], 2005.

Formula

Sum_{k=0..n+2} = 2*A033999(n+2).

Example

Triangle begins:
  -1, -1;
   0,  1,  1;
   0, -2, -1,  1;
   0,  2,  0, -1,  1;
   0, -2,  0,  0, -1,  1;
   0,  2,  0,  0,  0, -1,  1;
   0, -2,  0,  0,  0,  0, -1,  1;
   0,  2,  0,  0,  0,  0,  0, -1,  1;
   0, -2,  0,  0,  0,  0,  0,  0, -1,  1;
   0,  2,  0,  0,  0,  0,  0,  0,  0, -1,  1;
   0, -2,  0,  0,  0,  0,  0,  0,  0,  0, -1,  1;
   0,  2,  0,  0,  0,  0,  0,  0,  0,  0,  0, -1, 1;
   ...

Mathematica

p[x_, n_] = x*(x^n*(x - 1) + (-1)^n*2);
Table[CoefficientList[p[x, n], x], {n, -1, 10}]//Flatten

Prog

(Maxima) T(n, k) := ratcoef(x*(x^n*(x - 1) + (-1)^n*2), x, k)$
create_list(T(n, k), n, -1, 10, k, 0, n + 2); /* Franck Maminirina Ramaharo, Nov 02 2018 */

Crossrefs

Cf. A175739.

Sequence in context: A362899 A168261 A180997 * A105469 A257857 A339871

Adjacent sequences: A143436 A143437 A143438 * A143440 A143441 A143442

Keyword

sign,tabf

Author

Roger L. Bagula and Gary W. Adamson, Oct 23 2008

Extensions

Edited name, Joerg Arndt, May 26 2013

Offset corrected by Michel Marcus, May 27 2013

Status

approved