The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A143439

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A143439

Triangle whose n-th row is the expansion of x*(x^n*(x - 1) + (-1)^n*2).
(history; published version)

#19 by N. J. A. Sloane at Sat Nov 03 18:59:57 EDT 2018

STATUS

proposed

approved

#18 by Franck Maminirina Ramaharo at Sat Nov 03 15:24:01 EDT 2018

STATUS

editing

proposed

#17 by Franck Maminirina Ramaharo at Sat Nov 03 15:23:28 EDT 2018

CROSSREFS

Cf. A175739.

#16 by Franck Maminirina Ramaharo at Fri Nov 02 06:59:35 EDT 2018

COMMENTS

Row sums are: -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, -2, 2, ... .

LINKS

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

FORMULA

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

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 */

#15 by Franck Maminirina Ramaharo at Wed Oct 31 13:29:41 EDT 2018

LINKS

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.

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

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[%]

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

STATUS

approved

editing

#14 by Bruno Berselli at Mon May 27 05:03:47 EDT 2013

STATUS

reviewed

approved

#13 by Joerg Arndt at Mon May 27 04:07:34 EDT 2013

STATUS

proposed

reviewed

Discussion

Mon May 27

05:03

Bruno Berselli: Thanks!

#12 by Michel Marcus at Mon May 27 04:06:49 EDT 2013

STATUS

editing

proposed

#11 by Michel Marcus at Mon May 27 04:06:26 EDT 2013

EXTENSIONS

Offset corrected by Michel Marcus, May 27 2013

STATUS

proposed

editing

Discussion

Mon May 27

04:06

Michel Marcus: OK. Done.

#10 by Joerg Arndt at Sun May 26 12:22:30 EDT 2013

STATUS

editing

proposed

Discussion

Mon May 27

04:04

Bruno Berselli: Also "Offset corrected by Michel Marcus..." (I think).