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Search: id:A157981
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| A157981 |
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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}]. |
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1
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| 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; listen)
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OFFSET
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0,2
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COMMENT
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Row sums are:
{1, 22, 435, 8100, 145125, 2531250, 43284375, 729000000, 12131015625,
199905468750, 3267685546875,...}.
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REFERENCES
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Pegg, Ed Jr. "Witt Design," http://mathworld.wolfram.com/WittDesign.html
Weisstein, Eric W. "Block Design," http://mathworld.wolfram.com/BlockDesign.html
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FORMULA
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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))).
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EXAMPLE
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{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}
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MATHEMATICA
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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]
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CROSSREFS
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Sequence in context: A069890 A040550 A040551 this_sequence A040523 A040522 A040521
Adjacent sequences: A157978 A157979 A157980 this_sequence A157982 A157983 A157984
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KEYWORD
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sign,tabl,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 10 2009
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