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A078126
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Negative determinant of n X n matrix M_{i,j}=1 if i=j or i+j=1 (mod 2).
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4
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-1, -1, 0, 1, 3, 5, 8, 11, 15, 19, 24, 29, 35, 41, 48, 55, 63, 71, 80, 89, 99, 109, 120, 131, 143, 155, 168, 181, 195, 209, 224, 239, 255, 271, 288, 305, 323, 341, 360, 379, 399, 419, 440, 461, 483, 505, 528, 551, 575, 599, 624, 649, 675, 701, 728, 755, 783, 811
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OFFSET
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0,5
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COMMENTS
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Apparently, also 6(n+3) times the Dedekind sum s(2,n+3). - Ralf Stephan, Sep 16 2013
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LINKS
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FORMULA
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G.f.: (-1 + x + 2*x^2 - x^3) / ((1 - x^2) * (1 - x)^2).
a(n) = A024206(n-1) for all n in Z.
E.g.f.: ((x^2 + x - 4)*cosh(x) + (x^2 + x - 5)*sinh(x))/4. - Stefano Spezia, Aug 06 2024
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EXAMPLE
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G.f. = -1 - x + x^3 + 3*x^4 + 5*x^5 + 8*x^6 + 11*x^7 + 15*x^8 + 19*x^9 + ...
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MAPLE
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MATHEMATICA
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LinearRecurrence[{2, 0, -2, 1}, {-1, -1, 0, 1}, 60] (* Harvey P. Dale, Sep 10 2015 *)
a[n_]:=-Det[Table[If[i==j ||Mod[i+j, 2]==1, 1, 0], {i, n}, {j, n}]]; Join[{-1}, Array[a, 57]] (* Stefano Spezia, Aug 06 2024 *)
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PROG
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(PARI) a(n)=-matdet(matrix(n, n, i, j, i==j||((i+j)%2))) /* Ralf Stephan, Sep 16 2013 */
(PARI) a(n)=sumdedekind(2, n+3)*6*(n+3) /* Ralf Stephan, Sep 16 2013 */
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CROSSREFS
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KEYWORD
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sign,easy,nice
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AUTHOR
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EXTENSIONS
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A-number twister corrected in cross-refs by R. J. Mathar, Feb 11 2010
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STATUS
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approved
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