Search: id:A130617
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%I A130617
%S A130617 1,1,1,8,2,1,60,64,3,1,1232,688,1080,4,1,10192,51184,10584,18224,5,1,
%T A130617 72056802048,40202473760,63561929808,248790864,67127848,6,1,198067197911198400,
%U A130617 218306304849340800,9424712384162832,2565349679326160,72928609100,17313844512,
               7,1
%V A130617 1,1,-1,-8,-2,1,60,64,3,-1,1232,-688,-1080,-4,1,10192,-51184,10584,18224,
               5,-1,
%W A130617 -72056802048,40202473760,63561929808,248790864,-67127848,-6,1,198067197911198400,
%X A130617 218306304849340800,9424712384162832,-2565349679326160,-72928609100,17313844512,
               7,-1
%N 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.
%C A130617 Since not all the powers of two give primes, this sequences gets larger 
               than the autocorrelation matrix based sequence does.
%F A130617 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))
%e A130617 {1},
%e A130617 {1, -1},
%e A130617 {-8, -2, 1},
%e A130617 {60, 64, 3, -1},
%e A130617 {1232, -688, -1080, -4, 1},
%e A130617 {10192, -51184, 10584, 18224, 5, -1},
%e A130617 {-72056802048, 40202473760, 63561929808, 248790864, -67127848, -6,1}
%t A130617 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]
%Y A130617 Cf. A129964, A000668.
%Y A130617 Sequence in context: A157472 A147868 A073442 this_sequence A010150 A136711 
               A037920
%Y A130617 Adjacent sequences: A130614 A130615 A130616 this_sequence A130618 A130619 
               A130620
%K A130617 uned,sign
%O A130617 1,4
%A A130617 Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jun 18 2007

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