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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

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 * 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.)