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A157981 A triangle of coefficients of characteristic polynomials of a set of matrices: r=23;l=7;m(r,l,n)=(r - l)*IdentityMatrix[n] + l*Table[1, {i, 1, n}, {j, 1, n}]. 0
1, 23, -1, 480, -46, 1, 9472, -1440, 69, -1, 180224, -37888, 2880, -92, 1, 3342336, -901120, 94720, -4800, 115, -1, 60817408, -20054016, 2703360, -189440, 7200, -138, 1, 1090519040, -425721856, 70189056, -6307840, 331520, -10080, 161, -1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row sums are:

{1, 22, 435, 8100, 145125, 2531250, 43284375, 729000000, 12131015625,

199905468750, 3267685546875,...}.

REFERENCES

Pegg, Ed Jr. "Witt Design," http://mathworld.wolfram.com/WittDesign.html

Weisstein, Eric W. "Block Design," http://mathworld.wolfram.com/BlockDesign.html

LINKS

Table of n, a(n) for n=0..35.

FORMULA

r=23;l=7;m(r,l,n)=(r - l)*IdentityMatrix[n] + l*Table[1, {i, 1, n}, {j, 1, n}];

out_(n,m)=coefficient(characteristicpolynomial(m(23,7,n))).

EXAMPLE

{1},

{23, -1},

{480, -46, 1},

{9472, -1440, 69, -1},

{180224, -37888, 2880, -92, 1},

{3342336, -901120, 94720, -4800, 115, -1},

{60817408, -20054016, 2703360, -189440, 7200, -138, 1},

{1090519040, -425721856, 70189056, -6307840, 331520, -10080, 161, -1},

{19327352832, -8724152320, 1702887424, -187170816, 12615680, -530432, 13440, -184, 1},

{339302416384, -173946175488, 39258685440, -5108662272, 421134336, -22708224, 795648, -17280, 207, -1},

{5909874999296, -3393024163840, 869730877440, -130862284800, 12771655680, -842268672, 37847040, -1136640, 21600, -230, 1}

MATHEMATICA

Clear[M2, M, n, l, r];

M[r_, l_, n_] := (r - l)*IdentityMatrix[n] + l*Table[1, {i, 1, n}, {j, 1, n}];

r = 23; l = 7;

Join[{1}, Table[Expand[CharacteristicPolynomial[M[r, l, n], x]], {n, 1, 10}]];

a = Join[{{1}}, Table[CoefficientList[Expand[CharacteristicPolynomial[M[r, l, n], x]], x], {n, 1, 10}]];

Flatten[a]

CROSSREFS

Sequence in context: A069890 A040550 A040551 * A040523 A040522 A040521

Adjacent sequences:  A157978 A157979 A157980 * A157982 A157983 A157984

KEYWORD

sign,tabl,uned

AUTHOR

Roger L. Bagula, Mar 10 2009

STATUS

approved

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Last modified August 12 06:22 EDT 2020. Contains 336438 sequences. (Running on oeis4.)