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 A350710 Triangle read by rows formed from the coefficients in ascending order of the characteristic polynomial of the n X n matrix M(n) with entries M(n)[i,j] = i*j mod n+1. 0
 1, -1, 1, -3, -2, 1, -16, -16, -2, 1, 0, 100, -10, -10, 1, -1296, 0, 324, -24, -13, 1, 0, 0, 4116, 392, -175, -14, 1, 0, -131072, 16384, 12288, -512, -352, -12, 1, 0, 0, -708588, 0, 44469, 2592, -459, -24, 1, 0, 0, 16000000, 800000, -760000, -12000, 11000, -100, -45, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Table of n, a(n) for n=0..54. EXAMPLE Triangle begins: n=0: 1; n=1: -1, 1; n=2: -3, -2, 1; n=3: -16, -16, -2, 1; n=4: 0, 100, -10, -10, 1; n=5: -1296, 0, 324, -24, -13, 1; n=6: 0, 0, 4116, 392, -175, -14, 1; For example, the characteristic polynomial associated to M(7) is q^7 - 12*q^6 - 352*q^5 - 512*q^4 + 12288*q^3 + 16384*q^2 - 131072*q + 0; so the seventh row of the triangle is 0, -131072, 16384, 12288, -512, -352, -12, 1. MAPLE T:= n-> (p-> seq(coeff(p, x, i), i=0..n))(LinearAlgebra[ CharacteristicPolynomial](Matrix(n, (i, j)-> irem(i*j, n+1)), x)): seq(T(n), n=0..10); # Alois P. Heinz, Mar 27 2022 MATHEMATICA Table[(-1)^(p + 1)*CoefficientList[CharacteristicPolynomial[Table[Mod[k*Table[i, {i, 1, p - 1}], p], {k, 1, p - 1}], x], x], {p, 2, 20}] PROG (PARI) row(n) = Vecrev(charpoly(matrix(n, n, i, j, i*j%(n+1)))); \\ Kevin Ryde, Mar 27 2022 CROSSREFS Cf. A352620 (matrices M). Sequence in context: A248035 A088956 A106208 * A129377 A136733 A117269 Adjacent sequences: A350707 A350708 A350709 * A350711 A350712 A350713 KEYWORD sign,tabl AUTHOR Luca Onnis, Mar 27 2022 STATUS approved

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Last modified December 11 09:49 EST 2023. Contains 367722 sequences. (Running on oeis4.)