login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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. 0
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 (list; table; graph; refs; listen; history; text; internal format)
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: A344276 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 23 20:42 EDT 2021. Contains 347617 sequences. (Running on oeis4.)