1,5

Row sums are: {0, 2, 4, 16, 48, 110, 512, 572, 3360, 7616, 26070, 9968, 365184, 36814, 1532128, 4848280, 16897440, 437578, 228446272, 1438264, 1596986490, ...}

This tensor like approach is based on the operational ideas of Gary W. Adamson:

Thinking about triangular sequences as triangular tensors and Adamson's

operations on them as a new kind of "operator"calculus:

Operator.T[n,m]=T'[n,m]

The idea is that

since some of these triangular sequences are representations of

orthogonal / Hilbert space wave functions as polynomials

there should be a Hamiltonian:

H.T[n,m]=E[n].T[n,m]

where E[n] is an energy vector.

That approach opens up vector operators of the sort:

T[n,m].V[n]=T'[n,m]

The current sequence is a result of just such an operation.

T(n,m)=a(n).t(n,m); a(n)=Fibonacci(n): t(n,m)=Binomial(n,GCD(n,m)).

{0},

{1, 1},

{1, 2, 1},

{2, 6, 6, 2},

{3, 12, 18, 12, 3},

{5, 25, 25, 25, 25, 5},

{8, 48, 120, 160, 120, 48, 8},

{13, 91, 91, 91, 91, 91, 91, 13},

{21, 168, 588, 168, 1470, 168, 588, 168, 21},

{34, 306, 306, 2856, 306, 306, 2856, 306, 306, 34},

{55, 550, 2475, 550, 2475, 13860, 2475, 550, 2475, 550, 55}

Clear[t, a, n, m] t[n_, m_] = Binomial[n, GCD[n, m]]; a = Table[Table[Fibonacci[n]*t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[a]

Cf. A000045.

Sequence in context: A151962 A072137 A061569 this_sequence A094965 A025277 A153896

Adjacent sequences: A140832 A140833 A140834 this_sequence A140836 A140837 A140838

nonn,tabl,uned

Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Jul 18 2008