A140326 Sign weighted matrices n X n:example {{2 w[2], w[0], w[1]}, {3 w[0], 2 w[1], w[2]}, {3 w[1], 3 w[2], 2 w[0]}} are made into monomials using w[n]=1 if n<>0, x if n==0. The coefficients of the monomials form a triangular sequence.

1, 0, 2, -3, 0, 4, -12, 20, 0, -6, 24, -84, 73, 0, -12, 48, -256, 408, -216, 0, 18, -48, 480, -1328, 1464, -603, 0, 36, 0, 704, -3312, 5760, -4500, 1404, 0, -54, -192, 0, 4720, -15264, 20520, -13212, 3537, 0, -108, -768, 3584, 0, -26880, 62496, -64512, 33264, -7344, 0, 162, 1536, -12288, 29440, 0, -116256

Offset

1,3

Comments

Row sums:

{1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1}.

Links

Table of n, a(n) for n=1..60.

Formula

Matrix: M(d)=(2 + Sign[n - m])*w[Mod[n + m, d]; If[n == 0, w[n] = x, w[n] = 1]; out_n,m=Coefficients[Det(M(d)))

Example

{1},
{0, 2},
{-3, 0, 4},
{-12, 20, 0, -6},
{24, -84, 73, 0, -12},
{48, -256,408, -216, 0, 18},
{-48, 480, -1328, 1464, -603, 0, 36},
{0, 704, -3312, 5760, -4500,1404, 0, -54},
{-192, 0, 4720, -15264, 20520, -13212, 3537, 0, -108},
{-768, 3584, 0, -26880, 62496, -64512, 33264, -7344, 0, 162},
{1536, -12288, 29440, 0, -116256, 221760, -195552, 88560, -17523, 0, 324}

Mathematica

M[d_] := Table[(2 + Sign[n - m])*w[Mod[n + m, d]], {n, 1, d}, {m, 1, d}]; a = Table[M[d], {d, 1, 10}]; Table[If[n == 0, w[n] = x, w[n] = 1], {n, 0, 10}]; Table[Det[a[[d]]], {d, 1, 10}]; a0 = Join[{{1}}, Table[CoefficientList[Det[a[[d]]], x], {d, 1, 10}]]; Flatten[a0] Table[Apply[Plus, CoefficientList[Det[a[[d]]], x]], {d, 1, 10}];

Crossrefs

Sequence in context: A363966 A258818 A261275 * A261781 A211402 A256064

Adjacent sequences: A140323 A140324 A140325 * A140327 A140328 A140329

Keyword

uned,tabl,sign

Author

Roger L. Bagula and Gary W. Adamson, May 26 2008

Status

approved