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A213234 Triangle read by rows: coefficients of auxiliary Rudin-Shapiro polynomials A_{ns}(omega) written in descending powers of x. 1
2, 1, 1, -2, 1, -3, 1, -4, 2, 1, -5, 5, 1, -6, 9, -2, 1, -7, 14, -7, 1, -8, 20, -16, 2, 1, -9, 27, -30, 9, 1, -10, 35, -50, 25, -2, 1, -11, 44, -77, 55, -11, 1, -12, 54, -112, 105, -36, 2, 1, -13, 65, -156, 182, -91, 13, 1, -14, 77, -210, 294, -196, 49, -2, 1, -15, 90, -275, 450, -378, 140, -15 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

REFERENCES

Brillhart, John; Lomont, J. S.; Morton, Patrick. Cyclotomic properties of the Rudin-Shapiro polynomials. J. Reine Angew. Math.288 (1976), 37--65. See Table 1. MR0498479 (58 #16589).

LINKS

Table of n, a(n) for n=0..71.

FORMULA

T(n,k) = (-1)^k*A034807(n,k). - Philippe Deléham , Nov 10 2013

EXAMPLE

The first few polynomials are:

2

x

x^2-2

x^3-3*x

x^4+2-4*x^2

x^5-5*x^3+5*x

x^6-2-6*x^4+9*x^2

x^7-7*x^5+14*x^3-7*x

x^8+2-8*x^6+20*x^4-16*x^2

x^9-9*x^7+27*x^5-30*x^3+9*x

x^10-2-10*x^8+35*x^6-50*x^4+25*x^2

x^11-11*x^9+44*x^7-77*x^5+55*x^3-11*x

x^12+2-12*x^10+54*x^8-112*x^6+105*x^4-36*x^2

...

Triangle begins:

[2]

[1]

[1, -2]

[1, -3]

[1, -4, 2]

[1, -5, 5]

[1, -6, 9, -2]

[1, -7, 14, -7]

[1, -8, 20, -16, 2]

[1, -9, 27, -30, 9]

[1, -10, 35, -50, 25, -2]

[1, -11, 44, -77, 55, -11]

[1, -12, 54, -112, 105, -36, 2]

...

MAPLE

#The program is valid for n>=1:

f:=n->x^n+add((-1)^i*(n/i)*binomial(n-i-1, i-1)*x^(n-2*i), i=1..floor(n/2));

g:=n->series(x^n*subs(x=1/x, f(n)), x, n+1);

h:=n->seriestolist(series(subs(x=sqrt(x), g(n)), x, n+1));

for n from 0 to 15 do lprint(h(n)); od:

CROSSREFS

Cf. A132460.

Sequence in context: A050221 A213235 A113279 * A034807 A275111 A182961

Adjacent sequences:  A213231 A213232 A213233 * A213235 A213236 A213237

KEYWORD

sign,tabf

AUTHOR

N. J. A. Sloane, Jun 06 2012

STATUS

approved

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Last modified February 19 12:48 EST 2018. Contains 299333 sequences. (Running on oeis4.)