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 A078126 Negative determinant of n X n matrix M_{i,j}=1 if i=j or i+j=1 (mod 2). 3
 -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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Apparently, also 6(n+3) times the Dedekind sum s(2,n+3). - Ralf Stephan, Sep 16 2013 LINKS Table of n, a(n) for n=0..57. Moira Chas, Anthony Phillips, Self-intersection numbers of curves in the doubly-punctured plane , arXiv:1001.4568 [math.GT], 2010. [Jonathan Vos Post, Jan 27 2010] Eric Weisstein's World of Mathematics, Dedekind Sum Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1). FORMULA G.f.: (-1 + x + 2*x^2 - x^3) / ((1 - x^2) * (1 - x)^2). a(n) = A002620(n) - 1. a(n) = A002623(n-2) - A002623(n-3) - 1. a(n) = A024206(n-1) for all n in Z. a(n) = floor( (n+2)(n-2)/4 ). - Wesley Ivan Hurt, Jun 16 2013 A004526(n) = a(n) - a(n-1) for all n in Z. - Michael Somos, Aug 22 2016 a(n) = Sum_{i=1..n+2} floor((n-i+1)/2). - Wesley Ivan Hurt, Sep 12 2017 EXAMPLE G.f. = -1 - x + x^3 + 3*x^4 + 5*x^5 + 8*x^6 + 11*x^7 + 15*x^8 + 19*x^9 + ... MAPLE A078126:=n->floor((n + 2)*(n - 2)/4); seq(A078126(n), n=0..100); # Wesley Ivan Hurt, Jan 30 2014 MATHEMATICA Table[Floor[(n + 2)(n - 2)/4], {n, 0, 100}] (* Wesley Ivan Hurt, Jan 30 2014 *) LinearRecurrence[{2, 0, -2, 1}, {-1, -1, 0, 1}, 60] (* Harvey P. Dale, Sep 10 2015 *) PROG (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 */ CROSSREFS Cf. A002620, A002623, A004526, A024206. Sequence in context: A219656 A024169 A213706 * A024206 A159325 A228848 Adjacent sequences: A078123 A078124 A078125 * A078127 A078128 A078129 KEYWORD sign,easy,nice AUTHOR Michael Somos, Nov 18 2002 EXTENSIONS A-number twister corrected in cross-refs by R. J. Mathar, Feb 11 2010 STATUS approved

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Last modified April 25 09:38 EDT 2024. Contains 371967 sequences. (Running on oeis4.)