login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A155582 A designed triangular sequence based on four sequences using the binomial and Catalan numbers. 1
1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 2, 7, 2, 1, 1, 3, 3, 3, 3, 1, 1, 6, 9, 20, 9, 6, 1, 1, 7, 21, 35, 35, 21, 7, 1, 1, 8, 28, 56, 70, 56, 28, 8, 1, 1, 5, 36, 84, 126, 126, 84, 36, 5, 1, 1, 10, 25, 120, 210, 252, 210, 120, 25, 10, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

row sums are:

{1, 2, 4, 8, 13, 14, 52, 128, 256, 504, 984,...}.

First sequence choice is the Catalan, next the lowest, next the highest and

last, the factorial as the binomial.

The effort in designing this sequence was to demonstrate

how a multi-bifurcative process like that seen in the Eulerian numbers

and MacMahon numbers might work.

LINKS

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

FORMULA

Catalan:

a(n)=((4*n - 2)/(n + 1))*a(n - 1);

Highest:

a(n)=If[IntegerQ[((6*n - 4)/( n + 1))*a(n - 1)], ((6*n - 4)/(n + 1))* a(n - 1), If[IntegerQ[((4*n - 2)/(n + 1))*a( n - 1)], ((4*n - 2)/(n + 1))*a(n - 1), n*a(n - 1)]] ;

Lowest:

a(n)=If[IntegerQ[((3*n - 2)/( n + 1))*a(n - 1)], ((3*n - 2)/(n + 1))* a(n - 1), If[IntegerQ[((4*n - 2)/(n + 1))*a( n - 1)], ((4*n - 2)/(n + 1))*a(n - 1), n*a(n - 1)]]

EXAMPLE

{1},

{1, 1},

{1, 2, 1},

{1, 3, 3, 1},

{1, 2, 7, 2, 1},

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

{1, 6, 9, 20, 9, 6, 1},

{1, 7, 21, 35, 35, 21, 7, 1},

{1, 8, 28, 56, 70, 56, 28, 8, 1},

{1, 5, 36, 84, 126, 126, 84, 36, 5, 1},

{1, 10, 25, 120, 210, 252, 210, 120, 25, 10, 1}

MATHEMATICA

Clear [a, b, c, n];

a[0] = 1;

a[n_] := a[n] = ((4*n - 2)/(n + 1))*a[n - 1];

b[0] = 1;

b[n_] := b[n] = If[IntegerQ[((3*n - 2)/(n + 1))*b[n - 1]], ((3*n - 2)/(n + 1))*b[n - 1], If[IntegerQ[((4*n - 2)/( n + 1))*b[n - 1]], ((4*n - 2)/(n + 1))*b[n - 1], n*b[n - 1]]];

c[0] = 1;

c[n_] := c[n] = If[IntegerQ[((6*n - 4)/(n + 1))*c[n - 1]], ((6*n - 4)/(n + 1))*c[n - 1], If[IntegerQ[((4*n - 2)/(n + 1))*c[n - 1]], ((4*n - 2)/(n + 1))*c[n - 1], n*c[n - 1]]];

t[n_, m_] := t[n, m] = If[IntegerQ[a[n]/(a[m]*a[n - m])], a[n]/(a[m]*a[n - m]), If[IntegerQ[b[ n]/(b[m]*b[n - m])], b[n]/(b[m]* b[n - m]), If[IntegerQ[ c[n]/(c[m]*c[n - m])], c[n]/(c[m]*c[n - m]), Binomial[n, m]]]];

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

Flatten[%]

CROSSREFS

Sequence in context: A204087 A080381 A080396 * A169946 A160832 A157458

Adjacent sequences:  A155579 A155580 A155581 * A155583 A155584 A155585

KEYWORD

nonn,uned

AUTHOR

Roger L. Bagula, Jan 24 2009

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 23 23:03 EST 2018. Contains 299595 sequences. (Running on oeis4.)