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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 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 October 20 16:00 EDT 2019. Contains 328267 sequences. (Running on oeis4.)