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 A130617 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. 0
 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; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Since not all the powers of two give primes, this sequences gets larger than the autocorrelation matrix based sequence does. LINKS FORMULA 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)) EXAMPLE {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} MATHEMATICA 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] CROSSREFS Cf. A129964, A000668. Sequence in context: A147868 A073442 A177428 * A010150 A176153 A136711 Adjacent sequences:  A130614 A130615 A130616 * A130618 A130619 A130620 KEYWORD uned,sign AUTHOR Roger L. Bagula, Jun 18 2007 STATUS approved

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Last modified July 25 20:59 EDT 2021. Contains 346294 sequences. (Running on oeis4.)