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A172453 A combinatorial triangle based on A004001 product sequences:c(n)=If[n == 1, 1, Product[A004001[m], {m, 1, n}]];t(n,m)=c(n)/(c(m)*c(n-m)) 0
1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 4, 2, 1, 1, 3, 6, 6, 3, 1, 1, 4, 12, 12, 12, 4, 1, 1, 4, 16, 24, 24, 16, 4, 1, 1, 4, 16, 32, 48, 32, 16, 4, 1, 1, 5, 20, 40, 80, 80, 40, 20, 5, 1, 1, 6, 30, 60, 120, 160, 120, 60, 30, 6, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

Row sums are:

{1, 2, 3, 6, 10, 20, 46, 90, 154, 292, 594,...}.

The Modulo two pattern appears to be symmetrically chaotic:

ListDensityPlot[Table[Table[If[n >= m, Mod[t[ n, m], 2], 0], {m, 0, 32}], {n, 0, 32}], Mesh -> False, Axes -> False]

LINKS

Table of n, a(n) for n=0..65.

FORMULA

c(n)=If[n == 1, 1, Product[A004001[m], {m, 1, n}]]

t(n,m)=c(n)/(c(m)*c(n-m))

EXAMPLE

{1},

{1, 1},

{1, 1, 1},

{1, 2, 2, 1},

{1, 2, 4, 2, 1},

{1, 3, 6, 6, 3, 1},

{1, 4, 12, 12, 12, 4, 1},

{1, 4, 16, 24, 24, 16, 4, 1},

{1, 4, 16, 32, 48, 32, 16, 4, 1},

{1, 5, 20, 40, 80, 80, 40, 20, 5, 1},

{1, 6, 30, 60, 120, 160, 120, 60, 30, 6, 1}}

MATHEMATICA

(*A004001*)

f[0] = 0; f[1] = 1; f[2] = 1;

f[n_] := f[n] = f[f[n - 1]] + f[n - f[n - 1]];

c[n_] := If[n == 1, 1, Product[f[m], {m, 1, n}]];

t[n_, m_] := c[n]/(c[m]*c[n - m]);

Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];

Flatten[%]

CROSSREFS

A004001

Sequence in context: A220777 A088855 A034851 * A172479 A122085 A209612

Adjacent sequences:  A172450 A172451 A172452 * A172454 A172455 A172456

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Feb 03 2010

STATUS

approved

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Last modified October 19 18:28 EDT 2018. Contains 316377 sequences. (Running on oeis4.)