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}}.

1, 0, 7, 52, 189, 496, 1075, 2052, 3577, 5824, 8991, 13300, 18997, 26352, 35659, 47236, 61425, 78592, 99127, 123444, 151981, 185200, 223587, 267652, 317929, 374976, 439375, 511732, 592677, 682864, 782971, 893700, 1015777, 1149952, 1296999, 1457716, 1632925

Offset: 1

Author

Artur Jasinski, Mar 31 2008

Keywords

• nonn
• easy

Links

• Eric Weisstein's World of Mathematics, Alexander Polynomial.

Crossrefs

Cf. A002061.

Programs

Magma

[n^4-5*n^3+9*n^2-8*n+4: n in [1..40]]; // Vincenzo Librandi, Nov 22 2015

Maple

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

Mathematica

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}]
(* 2nd program *)
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 *)

PARI

vector(40, n, n^4-5*n^3+9*n^2-8*n+4) \\ Altug Alkan, Nov 22 2015

Formula

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}}].

a(n) = (n^2-n+1)*(n-2)^2. - Artur Jasinski, Apr 05 2008

G.f.: x*(1 - 5*x + 17*x^2 + 7*x^3 + 4*x^4)/(1-x)^5. - Vincenzo Librandi, Nov 22 2015