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%I #3 Mar 30 2012 17:34:21
%S 1,1,-1,-8,-2,1,60,64,3,-1,1232,-688,-1080,-4,1,10192,-51184,10584,
%T 18224,5,-1,-72056802048,40202473760,63561929808,248790864,-67127848,
%U -6,1,198067197911198400,218306304849340800,9424712384162832,-2565349679326160,-72928609100,17313844512,7,-1
%N 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 Since not all the powers of two give primes, this sequences gets larger than the autocorrelation matrix based sequence does.
%F 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 {1},
%e {1, -1},
%e {-8, -2, 1},
%e {60, 64, 3, -1},
%e {1232, -688, -1080, -4, 1},
%e {10192, -51184, 10584, 18224, 5, -1},
%e {-72056802048, 40202473760, 63561929808, 248790864, -67127848, -6,1}
%t 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 Cf. A129964, A000668.
%K uned,sign
%O 1,4
%A _Roger L. Bagula_, Jun 18 2007
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