0,4

Row sums are:

{0, -1, -2, 0, -4, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0,...}.

The absolute values of the row sums are:

{0, 1, 2, 6, 4, 10, 12, 28, 8, 18, 20, 44, 24, 52, 56, 120,...}.

In a quantum Heisenberg matrix mechanics based on the triangular Hadamards

where the H(n) behave like wave functions Phi(n), these polynomials

are equivalent to the time dependent differentials:

Hamiltonian.Phi(n)=-Hbar*I*dPhi(n)/dt

Sum of the kth row polynomial:

p(x,n)=If[n>2^m,Sum[H(2^m)[[k]]*x^(1-k),{k,1,n}]];

t(n,l)=coefficients(p(x,n),x)

{0},

{-1},

{0, -2},

{-1, -2, 3},

{0, 0, 0, -4},

{-1, 0, 0, -4, 5},

{0, -2, 0, -4, 0, 6},

{-1, -2, 3, -4, 5, 6, -7},

{ 0, 0, 0, 0, 0, 0, 0, -8},

{-1, 0, 0, 0, 0, 0, 0, -8, 9},

{0, -2, 0, 0, 0, 0, 0, -8, 0, 10},

{-1, -2, 3, 0, 0, 0, 0, -8, 9, 10, -11},

{0, 0, 0, -4, 0, 0, 0, -8, 0, 0, 0, 12},

{-1, 0, 0, -4, 5, 0, 0, -8, 9, 0, 0, 12, -13},

{0, -2, 0, -4, 0, 6, 0, -8, 0, 10, 0, 12, 0, -14},

{-1, -2, 3, -4, 5, 6, -7, -8, 9, 10, -11, 12, -13, -14, 15}

Clear[HadamardMatrix];

MatrixJoinH[A_, B_] := Transpose[Join[Transpose[A], Transpose[B]]];

KroneckerProduct[M_, N_] := Module[{M1, N1, LM, LN, N2},

M1 = M;

N1 = N;

LM = Length[M1];

LN = Length[N1];

Do[M1[[i, j]] = M1[[i, j]]N1, {i, 1, LM}, {j, 1, LM}];

Do[M1[[i, 1]] = MatrixJoinH[M1[[i, 1]], M1[[i, j]]], {j, 2, LM}, {i, 1, LM}];

N2 = {};

Do[AppendTo[N2, M1[[i, 1]]], {i, 1, LM}];

N2 = Flatten[N2];

Partition[N2, LM*LN, LM*LN]]

HadamardMatrix[2] := {{1, 0}, {1, -1}};

HadamardMatrix[n_] := Module[{m}, m = {{1, 0}, {1, -1}}; KroneckerProduct[m, HadamardMatrix[n/2]]];

M = HadamardMatrix[16];

Table[D[Sum[M[[n]][[m]]*x^(m - 1), {m, 1, n}], {x, 1}], {n, 1, Length[M]}];

Table[CoefficientList[D[Sum[ M[[n]][[m]]*x^(m - 1), {m, 1, n}], {x, 1}], x], {n, 1, Length[M]}];

Flatten[%]

A158800

Sequence in context: A092186 A138262 A127510 this_sequence A129390 A129391 A123590

Adjacent sequences: A158807 A158808 A158809 this_sequence A158811 A158812 A158813

sign,tabl,uned

Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Mar 27 2009