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 A359559 a(n) is the determinant of an n X n Hermitian Toeplitz matrix whose first row consists of 1, 2*i, ..., n*i, where i denotes the imaginary unit. 7
 1, 1, -3, -16, -36, -40, 20, 184, 400, 432, -112, -1472, -3136, -3328, 576, 9856, 20736, 21760, -2816, -59392, -123904, -129024, 13312, 333824, 692224, 716800, -61440, -1785856, -3686400, -3801088, 278528, 9207808, 18939904, 19464192, -1245184, -46137344, -94633984 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Wikipedia, Toeplitz Matrix FORMULA A359614(n) <= a(n) <= A359615(n). Conjectured formulas: (Start) O.g.f.: (1 - 5*x + 9*x^2 - 12*x^3 + 10*x^4 - 4*x^5)/(1 - 2*x + 2*x^2)^3. a(n) = 6*a(n-1) - 18*a(n-2) + 32*a(n-3) - 36*a(n-4) + 24*a(n-5) - 8*a(n-6) for n > 5. E.g.f.: (2 + exp(x)*((1 + x)*(2 + x)*cos(x) - (1 + x + x^2)*sin(x)))/4. (End) EXAMPLE a(3) = -16: [ 1, 2*i, 3*i; -2*i, 1, 2*i; -3*i, -2*i, 1 ] MATHEMATICA Join[{1}, Table[Det[ToeplitzMatrix[Join[{1}, I Range[2, n]]]], {n, 36}]] PROG (PARI) a(n) = matdet(matrix(n, n, i, j, if (i==j, 1, if (ij else -1) if i!=j else I for i in range(n) for j in range(n)]).det()*(1, -I, -1, I)[n&3] # Chai Wah Wu, Jan 25 2023 CROSSREFS Cf. A001792 (symmetric Toeplitz matrix), A143182. Cf. A359560 (permanent), A359561, A359562. Cf. A359614 (minimal), A359615 (maximal). Sequence in context: A013199 A162419 A322191 * A076153 A031302 A217130 Adjacent sequences: A359556 A359557 A359558 * A359560 A359561 A359562 KEYWORD sign AUTHOR Stefano Spezia, Jan 06 2023 STATUS approved

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Last modified March 27 05:46 EDT 2023. Contains 361554 sequences. (Running on oeis4.)