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 A337966 Triangle read by rows, coefficients of polynomials over {-1, 0, 1}. Also a triangle-to-triangle transformation U -> T(U) applied to the triangle U(n, k) = 1. 4
 1, 1, 0, -1, -1, 1, 0, -1, 0, 1, -1, 1, 1, -1, -1, -1, 0, 1, 0, -1, 0, 1, 1, -1, -1, 1, 1, -1, 0, 1, 0, -1, 0, 1, 0, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0 COMMENTS The triangle can also be seen as a generalization of A118828. LINKS FORMULA Let polynomials P(n, z) be defined by: t(n, x) = Sum_{k=0..n} z^k*x^(n-k). s(n, x) = x^n*t(n, -x)/(1 - (-x))^(n+1). S(n, x) = x*(s(n, x) - s(n, -x)). Let i denote the imaginary unit. Then P(n, z) = (-2)^floor(n/2)*S(n, i) and T(n, k) = [z^k] P(n, z). EXAMPLE Triangle starts: [0]  1 [1]  1,  0 [2] -1, -1,  1 [3]  0, -1,  0,  1 [4] -1,  1,  1, -1, -1 [5] -1,  0,  1,  0, -1,  0 [6]  1,  1, -1, -1,  1,  1, -1 [7]  0,  1,  0, -1,  0,  1,  0, -1 [8]  1, -1, -1,  1,  1, -1, -1,  1, 1 [9]  1,  0, -1,  0,  1,  0, -1,  0, 1, 0 MAPLE A337966 := proc(n, k) [1, 1, -1, 0, -1, -1, 1, 0][irem(n + 2*k, 8) + 1] end: for n from 0 to 9 do lprint(seq(A337966(n, k), k=0..n)) od; CROSSREFS Cf. A118828 (diagonal, column 0 and row sum, with some shifts). Cf. A337967 (shows an interpretation as a transform). Sequence in context: A267778 A285384 A165728 * A010890 A011633 A015254 Adjacent sequences:  A337963 A337964 A337965 * A337967 A337968 A337969 KEYWORD sign,tabl AUTHOR Peter Luschny, Oct 04 2020 STATUS approved

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Last modified May 9 09:41 EDT 2021. Contains 343699 sequences. (Running on oeis4.)