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A141664 An irregular triangular sequence formed by partition-like complex polynomials. 1
1, 1, 0, 1, 0, 0, -1, 1, 0, 0, -1, -1, -1, 0, 1, 0, 0, -1, -1, -2, -1, -1, 0, 0, 1, 1, 0, 0, -1, -1, -2, -2, -2, -1, -1, 1, 1, 1, 1, 1, 0, 1, 0, 0, -1, -1, -2, -2, -3, -2, -2, 0, 0, 2, 2, 3, 2, 2, 1, 1, 0, 0, -1, 1, 0, 0, -1, -1, -2, -2, -3, -3, -3, -1, -1, 1, 2, 4, 4, 5, 4, 4, 3, 2, 0, 0, -1, -1, -1, -1, -1, 0, 1, 0, 0, -1, -1, -2, -2, -3, -3, -4, -2, -2, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,20

COMMENTS

Row sums are: {1, 1, 0, -2, -4, -4, 0, 8, 16, 16, 0, ...}.

LINKS

G. C. Greubel, Rows n=0..30 of triangle, flattened

FORMULA

Let p(x,n) = Product_{j=1..n} (1 + i*x^j), p(x,0)=1, with i being the imaginary unit, then the n-th row is the real part of the coefficients of p(x,n).

EXAMPLE

Irregular triangle begins as:

1.

1, 0.

1, 0, 0, -1.

1, 0, 0, -1, -1, -1,  0.

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

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

MATHEMATICA

p[x_, n_]:= If[n == 0, 1, Product[(1 + I*x^i), {i, 1, n}]];

Table[Expand[p[x, n]], {n, 0, 10}];

Table[Re[CoefficientList[p[x, n], x]], {n, 0, 10}]//Flatten

PROG

(PARI) row(n) = if (n==0, 1, apply(x->real(x), Vecrev(prod(j=1, n, (1 + I*x^j))))); \\ Michel Marcus, Apr 02 2019

CROSSREFS

Cf. A053632.

Sequence in context: A068934 A035200 A198066 * A056979 A087812 A288384

Adjacent sequences:  A141661 A141662 A141663 * A141665 A141666 A141667

KEYWORD

sign,look,tabf

AUTHOR

Roger L. Bagula, Sep 05 2008

EXTENSIONS

Edited by G. C. Greubel, Apr 01 2019

STATUS

approved

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Last modified September 29 07:08 EDT 2020. Contains 337425 sequences. (Running on oeis4.)