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 A301703 a(n) is the number of positive coefficients of the polynomial (x-1)*(x^2-1)*...*(x^n-1). 1
 1, 2, 3, 3, 6, 6, 9, 13, 16, 18, 21, 27, 34, 32, 42, 47, 54, 62, 73, 79, 85, 96, 104, 113, 123, 140, 150, 171, 174, 190, 200, 211, 234, 240, 263, 275, 301, 304, 322, 351, 368, 396, 413, 455, 451, 470, 487, 499, 531, 540, 592, 585, 631, 630, 687, 691, 734, 774, 793, 863 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 REFERENCES D. Andrica and O. Bagdasar, On some results concerning the polygonal polynomials, submitted to Carpathian Journal of Mathematics (2018). LINKS Michael De Vlieger, Table of n, a(n) for n = 1..300 Dorin Andrica, Ovidiu Bagdasar, On some results concerning the polygonal polynomials, Carpathian Journal of Mathematics (2019) Vol. 35, No. 1, 1-11. EXAMPLE Denote P_n(x) = (x-1)...(x^n-1). P_1(x) = x-1, hence a(1)=1. P_2(x) = (x-1)*(x^2-1) = x^3-x^2-x+1, hence a(2)=2; P_3(x) = (x-1)*(x^2-1)*(x^3-1) = x^6-x^5-x^4+x^2+x-1, hence a(3)=3; P_4(x) = (x-1)*(x^2-1)*(x^3-1)*(x^4-1) = x^10 - x^9 - x^8+2x^5-x^2-x+1, hence a(4)=3. MAPLE a:= n-> nops(select(x-> x>0, [(p-> seq(coeff(p, x, i), i=0..degree(p)))(expand(mul(x^i-1, i=1..n)))])): seq(a(n), n=1..60); # Alois P. Heinz, Mar 29 2019 MATHEMATICA Table[Count[CoefficientList[Expand[Times@@(x^Range[n]-1)], x], _?(#>0&)], {n, 60}] (* Harvey P. Dale, Feb 10 2019 *) PROG (PARI) a(n) = #select(x->(x>0), Vec((prod(k=1, n, (x^k-1))))); \\ Michel Marcus, Apr 02 2018 CROSSREFS Cf. A231599: a(n) is the number of positive coefficients in row n. Sequence in context: A222862 A101437 A039856 * A143715 A159685 A370804 Adjacent sequences: A301700 A301701 A301702 * A301704 A301705 A301706 KEYWORD nonn,easy AUTHOR Ovidiu Bagdasar, Mar 25 2018 STATUS approved

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