A129964 Triangular sequence produced from symmetrical power of two matrices of the general type: M={{1, 2, 4, 8}, {2, 1, 2, 4}, {4, 2, 1, 2}, {8, 4, 2, 1}}.

1, 1, -1, -3, -2, 1, 9, 21, 3, -1, -27, -108, -102, -4, 1, 81, 459, 810, 438, 5, -1, -243, -1782, -4617, -4932, -1797, -6, 1, 729, 6561, 22437, 36045, 26811, 7251, 7, -1, -2187, -23328, -99144, -213192, -242190, -136080, -29088, -8, 1, 6561, 80919, 411156, 1109052, 1702782, 1475010, 660420, 116460, 9

Offset

1,4

Comments

These matrices are related to symmetrical autocorrelation matrices. First column is alternating powers of 3. Absolute value row sum is ( new to OEIS too): Flatten[Join[{{1}}, Table[Apply[Plus,Abs[CoefficientList[CharacteristicPolynomial[ M[d, a], x], x]]], {d, 1, 10}]]]; {1, 2, 6, 34, 242, 1794, 13378, 99842, 745218, 5562370, 41518082}

References

MathRev083099.nb at Mathematica tutorial: http://www.arec.umd.edu/mathrev/LecturesMR99.ZIP/

Links

Table of n, a(n) for n=1..54.

Formula

I'm sorry the definition is not simpler, but this is what seems to work: define t(n, m, d, a) := If[n == m, 1, If[n - m <= d - 1 || m - n <= d - 1, a^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},
{-3, -2, 1},
{9, 21, 3, -1},
{-27, -108, -102, -4, 1},
{81, 459, 810, 438, 5, -1},
{-243, -1782, -4617, -4932, -1797, -6, 1}

Mathematica

t[n_, m_, d_, a_] := If[n == m, 1, If[n - m <= d - 1 || m - n <= d - 1, a^Abs[n - m], 0]]; M[d_, a_] := Table[t[n, m, d, a], {n, 1, d}, {m, 1, d}]; a = 2; a0 = Join[{{1}}, Table[CoefficientList[CharacteristicPolynomial[M[d, a], x], x], {d, 1, 10}]]; Flatten[a0]

Crossrefs

Sequence in context: A106338 A282628 A262554 * A267328 A267425 A267562

Adjacent sequences: A129961 A129962 A129963 * A129965 A129966 A129967

Keyword

uned,tabl,sign

Author

Roger L. Bagula, Jun 10 2007

Status

approved