A143439 - OEIS

%I #19 Nov 03 2018 18:59:57

%S -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,

%T 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,

%U 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

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

%H Eriko Hironaka, <a href="http://projecteuclid.org/euclid.ojm/1159189999">Salem-Boyd sequences and Hopf plumbing</a>, Osaka J. Math. Volume 43, Number 3 (2006), 497-516.

%H Eriko Hironaka, <a href="http://arxiv.org/abs/math/0506602v1">Salem-Boyd sequences and Hopf plumbing</a>, arXiv:math/0506602 [math.GT], 2005.

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

%e Triangle begins:

%e   -1, -1;

%e    0,  1,  1;

%e    0, -2, -1,  1;

%e    0,  2,  0, -1,  1;

%e    0, -2,  0,  0, -1,  1;

%e    0,  2,  0,  0,  0, -1,  1;

%e    0, -2,  0,  0,  0,  0, -1,  1;

%e    0,  2,  0,  0,  0,  0,  0, -1,  1;

%e    0, -2,  0,  0,  0,  0,  0,  0, -1,  1;

%e    0,  2,  0,  0,  0,  0,  0,  0,  0, -1,  1;

%e    0, -2,  0,  0,  0,  0,  0,  0,  0,  0, -1,  1;

%e    0,  2,  0,  0,  0,  0,  0,  0,  0,  0,  0, -1, 1;

%e    ...

%t p[x_, n_] = x*(x^n*(x - 1) + (-1)^n*2);

%t Table[CoefficientList[p[x, n], x], {n, -1, 10}]//Flatten

%o (Maxima) T(n, k) := ratcoef(x*(x^n*(x - 1) + (-1)^n*2), x, k)$

%o create_list(T(n, k), n, -1, 10, k, 0, n + 2); /* _Franck Maminirina Ramaharo_, Nov 02 2018 */

%Y Cf. A175739.

%K sign,tabf

%O -1,7

%A _Roger L. Bagula_ and _Gary W. Adamson_, Oct 23 2008

%E Edited name, _Joerg Arndt_, May 26 2013

%E Offset corrected by _Michel Marcus_, May 27 2013