2,1

Row sums are:

{2, 3, 3, 2, 5, 5, 2, 3, 7, 2,...},

The interesting effect is that the even terms are squares, and every third of them has (x+1).

m(n,m,d)=If[ n == m, 2, If[n == m - 1 || n == m + 1, -1, 0]];

p(x,n)=Characteristicpolynomial(m(n,m,k),x);

q(x,2*n,i)=Factor(p(x,2*n),i);

t(n,m)=coefficients(q(x,2*n,1))

Examples of polynomials (all):

x,

(1 + x)^2,

x^3,

(1 + x + x^2)^2,

x( 1 + x)^4,

(1 + x^2 + x^3)^2,

x^7,

(1 + x)^2(1 + x + x^3)^2,

x(1 + x + x^2)^4,

(1 + x + x^2 + x^4 + x^5)^2

Coefficients even first polynomials:

{1, 1},

{1, 1, 1},

{1, 0, 1, 1},

{1, 1},

{1, 1, 1, 0, 1, 1},

{1, 1, 0, 0, 1, 1, 1},

{1, 1},

{1, 1, 0, 0, 1},

{1, 1, 0, 0, 1, 1, 1, 0, 1, 1},

{1, 1}

Clear[M, T, d, a, x, a0];

T[n_, m_, d_] := If[ n == m, 2, If[n == m - 1 || n == m + 1, -1, 0]];

M[d_] := Table[T[n, m, d], {n, 1, d}, {m, 1, d}];

Table[FactorList[CharacteristicPolynomial[M[d], x], Modulus -> 2][[2]][[1]], {d, 2, 20, 2}];

Table[CoefficientList[FactorList[CharacteristicPolynomial[M[d], x], Modulus -> 2][[2]][[1]], x], {d, 2, 20, 2}];

Flatten[%]

Table[Apply[Plus, CoefficientList[FactorList[CharacteristicPolynomial[M[ d], x], Modulus -> 2][[2]][[1]], x]], {d, 2, 20, 2}];

Sequence in context: A152904 A118102 A089509 this_sequence A124897 A138345 A014590

Adjacent sequences: A157969 A157970 A157971 this_sequence A157973 A157974 A157975

nonn,tabl

Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Mar 10 2009