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Search: id:A130617
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| A130617 |
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Triangular sequence produced from symmetrical power of two matrices of the general type: M={{1, 3, 7, 31}, {3, 1, 3, 7}, {7, 3, 1, 3}, {31, 7, 3, 1}} with symmetrical primes of the type 2^n-1 A000668 instead of the 2^n of A129964. |
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+0
1
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| 1, 1, -1, -8, -2, 1, 60, 64, 3, -1, 1232, -688, -1080, -4, 1, 10192, -51184, 10584, 18224, 5, -1, -72056802048, 40202473760, 63561929808, 248790864, -67127848, -6, 1, 198067197911198400, 218306304849340800, 9424712384162832, -2565349679326160, -72928609100, 17313844512, 7, -1
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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Since not all the powers of two give primes, this sequences gets larger than the autocorrelation matrix based sequence does.
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FORMULA
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a0(n)=Primes of type 2^n-1=A000668[n] t(n, m, d, a) := If[n == m, 1, If[n - m <= d - 1 || m - n <= d - 1, a0[[Abs[n - m]]], 0]]; Matrix definition for general constant "a": M(d, a) := Table[t[n, m, d, a], {n, 1, d}, {m, 1, d}]; Constant: a=2; a(n)=CoefficientList(CharacteristicPloynomial(M(d,2))
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EXAMPLE
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{1},
{1, -1},
{-8, -2, 1},
{60, 64, 3, -1},
{1232, -688, -1080, -4, 1},
{10192, -51184, 10584, 18224, 5, -1},
{-72056802048, 40202473760, 63561929808, 248790864, -67127848, -6,1}
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MATHEMATICA
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a0 = Flatten[Table[If[PrimeQ[2^m - 1], 2^m - 1, {}], {m, 2, 127}]]; t[n_, m_, d_, a_] := If[n == m, 1, If[n - m <= d - 1 || m - n <= d - 1, a0[[ Abs[n - m]]], 0]]; M[d_, a_] := Table[t[n, m, d, a], {n, 1, d}, {m, 1, d}]; mm = Table[M[d, a], {d, 1, 10}]; TableForm[mm]; Table[CharacteristicPolynomial[M[d, a], x], {d, 1, 10}]; b0 = Join[{{1}}, Table[CoefficientList[CharacteristicPolynomial[M[d, a], x], x], {d, 1, 10}]]; Flatten[b0]
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CROSSREFS
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Cf. A129964, A000668.
Sequence in context: A157472 A147868 A073442 this_sequence A010150 A136711 A037920
Adjacent sequences: A130614 A130615 A130616 this_sequence A130618 A130619 A130620
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KEYWORD
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uned,sign
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jun 18 2007
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