1,2

a(n)=Sum[Signed_Pascal[n,k]*A000045(k)*Reverse(Coefficient(k,m)( Characteristic Polynomial(M(G_n)))),{k,n,m}]for n=m

Clear[a, b, f, c, f1, a1, b1, M, T, a0, b0, c0] size = 30; (* Pascal*) a = Table[Table[Binomial[n, m], {m, 0, n}], {n, 0, size}]; f[n_] := Table[0, {i, 1, n}] (* Inverted matrix Pascal*) b = Inverse[Table[Join[a[[n]], f[Length[a] - n]], {n, 1, Length[a]}]]; (* E_n Cartan reversed*) a0[n_] := 2; b0[n_] := -1; c0[n_] := -1; T[n_, m_, d_] := If[ n == m, a0[n], If[n == m - 1 || n == m + 1 || n == m - 3 || n == m + 3, If[n == m - 1 && m < d, b0[m - 1], If[n == m + 1 && n < d, b0[n - 1], If[n == m - 3 || n == m + 3, If[n == m - 3 && m == d, c0[m - 3], If[n == m + 3 && n == d, c0[n - 3], 0]]]]]]] M[d_] := Table[ If[TrueQ[T[n, m, d] == Null], 0, T[n, m, d]], {n, 1, d}, {m, 1, d}]; a1 = Join[{{1}}, Table[ Reverse[CoefficientList[Det[M[d] - x*IdentityMatrix[d]], x]], {d, 1, size}]]; b1 = Table[Join[a1[[n]], f[Length[a1] - n]], {n, 1, Length[a1]}]; (*Fibonacci*) f1[0] = 0; f1[1] = 1; f1[n_] := f1[n] = f1[n - 1] + f1[n - 2]; c = Table[Sum[f1[k]*b[[n, k]]*b1[[k, m]], {k, n, m}], {n, 1, size + 1}, {m, 1, size + 1}]; Table[c[[n, n]], {n, 1, size + 1}]

Adjacent sequences: A137389 A137390 A137391 this_sequence A137393 A137394 A137395

Sequence in context: A094147 A117612 A109136 this_sequence A065131 A063581 A055044

uned,sign

Roger L. Bagula and Gary Adamson (rlbagulatftn(AT)yahoo.com), Apr 10 2008