cp's OEIS Frontend

A138849 a(n) = AlexanderPolynomial[n] defined as Det[Transpose[S]-n S] where S is Kronecker Product of two 2 X 2 Seifert matrices {{-1, 1}, {0, -1}} [X] {{-1, 1}, {0, -1}} = {{1, -1, -1, 1}, {0, 1, 0, -1}, {0, 0, 1, -1}, {0, 0, 0, 1}}.

%I A138849 #29 Apr 09 2025 04:20:41
%S A138849 1,0,7,52,189,496,1075,2052,3577,5824,8991,13300,18997,26352,35659,
%T A138849 47236,61425,78592,99127,123444,151981,185200,223587,267652,317929,
%U A138849 374976,439375,511732,592677,682864,782971,893700,1015777,1149952,1296999,1457716,1632925
%N A138849 a(n) = AlexanderPolynomial[n] defined as Det[Transpose[S]-n S] where S is Kronecker Product of two 2 X 2 Seifert matrices {{-1, 1}, {0, -1}} [X] {{-1, 1}, {0, -1}} = {{1, -1, -1, 1}, {0, 1, 0, -1}, {0, 0, 1, -1}, {0, 0, 0, 1}}.
%H A138849 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AlexanderPolynomial.html">Alexander Polynomial</a>.
%F A138849 a(n) = Det[Transpose[{{1, -1, -1, 1}, {0, 1, 0, -1}, {0, 0, 1, -1}, {0, 0, 0, 1}}] - n {{1, -1, -1, 1}, {0, 1, 0, -1}, {0, 0, 1, -1}, {0, 0, 0, 1}}].
%F A138849 a(n) = (n^2-n+1)*(n-2)^2. - _Artur Jasinski_, Apr 05 2008
%F A138849 G.f.: x*(1 - 5*x + 17*x^2 + 7*x^3 + 4*x^4)/(1-x)^5. - _Vincenzo Librandi_, Nov 22 2015
%p A138849 A138849:=n->n^4-5*n^3+9*n^2-8*n+4: seq(A138849(n), n=1..50); # _Wesley Ivan Hurt_, Nov 22 2015
%t A138849 S = {{1, -1, -1, 1}, {0, 1, 0, -1}, {0, 0, 1, -1}, {0, 0, 0, 1}}; Table[Det[Transpose[S] - n S], {n, 0, 30}]
%t A138849 (* 2nd program *)
%t A138849 CoefficientList[Series[(1 - 5 x + 17 x^2 + 7 x^3 + 4 x^4)/(1 - x)^5, {x, 0, 40}], x] (* _Vincenzo Librandi_, Nov 22 2015 *)
%o A138849 (Magma) [n^4-5*n^3+9*n^2-8*n+4: n in [1..40]]; // _Vincenzo Librandi_, Nov 22 2015
%o A138849 (PARI) vector(40, n, n^4-5*n^3+9*n^2-8*n+4) \\ _Altug Alkan_, Nov 22 2015
%Y A138849 Cf. A002061.
%K A138849 nonn,easy
%O A138849 1,3
%A A138849 _Artur Jasinski_, Mar 31 2008