A071769 Determinant of the n X n matrix whose element (i,j) equals |i-j| (mod 4).
0, -1, 4, -12, -64, -208, 1088, -960, -8192, -6400, 58368, -27648, -344064, -151552, 1982464, -638976, -10485760, -3211264, 54788096, -13369344, -272629760, -63963136, 1346371584, -264241152, -6442450944, -1224736768, 30668750848
Offset: 1
Links
- Index entries for linear recurrences with constant coefficients, signature (0,-4,0,32,0,128,0,-256,0,-1024).
Crossrefs
Cf. A071768 (with mod 3).
Programs
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Maple
seq(LinearAlgebra:-Determinant(Matrix(n,n,(i,j) -> abs(i-j) mod 4)), n=1..100); # Robert Israel, Sep 29 2014
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Mathematica
Table[ Det[ Table[ Mod[ Abs[i - j], 4], {i, 1, n}, {j, 1, n}]], {n, 1, 30}] LinearRecurrence[{0,-4,0,32,0,128,0,-256,0,-1024},{0,-1,4,-12,-64,-208,1088,-960,-8192,-6400},30] (* Harvey P. Dale, Nov 28 2024 *) -
PARI
vector(30, n, matdet(matrix(n, n, i, j, abs(i-j)%4))) \\ Colin Barker, Sep 29 2014
Formula
a(4n+1) = (-1)*2^(4*n+2)*n*(3*n-2), a(4n+2) = (-1)*2^(4*n)*(12*n+1), a(4n+3) = 2^(4*n+2)*(12*n^2+4*n+1), a(4n+4) = (-1)*2^(4*n+2)*(12*n+3). 2*abs(a(n-1)) = A087982(n) for n=2, 3, 4, 5. - Benoit Cloitre, Nov 07 2003
G.f.: -x^2*(2304*x^8 + 2304*x^7 + 1280*x^6 - 704*x^5 + 224*x^4 + 48*x^3 + 16*x^2 - 4*x + 1) / ((2*x-1)^2*(2*x+1)^2*(4*x^2+1)^3). - Colin Barker, Sep 29 2014
E.g.f.: -9/4 + ((3/2)*x^2 - 15/8)*sin(2*x) + ((11/4)*x + 1/2)*cos(2*x) + ((3/4)*x + 5/8)*exp(-2*x) + (-(3/4)*x + 9/8)*exp(2*x). - Robert Israel, Sep 29 2014