A141605 Combination-like triangle of coefficients made using Somos(6) ;A006722; t(n,m)=A006722(n)/(A006722(n-m)*A006722(m)).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 3, 3, 1, 1, 2, 5, 5, 5, 5, 2, 1, 1, 2, 3, 9, 9, 9, 3, 2, 1, 1, 3, 5, 8, 23, 23, 8, 5, 3, 1, 1, 3, 8, 15, 25, 75, 25, 15, 8, 3, 1

Offset

1,23

Comments

Row sums are:

{1, 2, 3, 4, 5, 6, 17, 26, 39, 80, 179}.

Links

Table of n, a(n) for n=1..66.

Formula

t(n,m)=A006722(n)/(A006722(n-m)*A006722(m)).

Example

{1},
{1, 1},
{1, 1, 1},
{1, 1, 1, 1},
{1, 1, 1, 1, 1},
{1, 1, 1, 1, 1, 1},
{1, 3, 3, 3, 3, 3, 1},
{1, 2, 5, 5, 5, 5, 2, 1},
{1, 2, 3, 9, 9, 9, 3, 2, 1},
{1, 3, 5, 8, 23, 23, 8, 5, 3, 1},
{1, 3, 8, 15, 25, 75, 25, 15, 8, 3, 1}

Mathematica

Clear[a, t] (*A006722*) a[0] = a[1] =a[2] = a[3] = a[4] = a[5] = 1; a[n_] := a[n] = (a[n - 1]*a[n - 5] + a[n - 2]*a[ n - 4] + a[n - 3]^2)/a[n - 6]; Array[a, 23]; t[n_, m_] := a[n]/(a[n - m]*a[m]) Table[Table[Round[t[n, m]], {m, 0, n}], {n, 0, 10}]; Flatten[%]

Crossrefs

Cf. A006722.

Sequence in context: A177228 A247655 A097675 * A356002 A251551 A073139

Adjacent sequences: A141602 A141603 A141604 * A141606 A141607 A141608

Keyword

nonn,uned,tabl

Author

Roger L. Bagula and Gary W. Adamson, Aug 21 2008

Status

approved