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.

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

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

Table of n, a(n) for n=1..36.

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 * A362662 A010150 A176153

Adjacent sequences: A130614 A130615 A130616 * A130618 A130619 A130620

Keyword

uned,sign

Author

Roger L. Bagula, Jun 18 2007

Status

approved