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

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A047072 Array T read by diagonals: T(h,k)=number of paths consisting of steps from (0,0) to (h,k) such that each step has length 1 directed up or right and no step touches the line y=x unless x=0 or x=h. 21
1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 3, 2, 2, 3, 1, 1, 4, 5, 4, 5, 4, 1, 1, 5, 9, 5, 5, 9, 5, 1, 1, 6, 14, 14, 10, 14, 14, 6, 1, 1, 7, 20, 28, 14, 14, 28, 20, 7, 1, 1, 8, 27, 48, 42, 28, 42, 48, 27, 8, 1, 1, 9, 35, 75, 90, 42, 42, 90, 75, 35, 9, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..77.

R. K. Guy, Catwalks, Sandsteps and Pascal Pyramids, J. Integer Seqs., Vol. 3 (2000), #00.1.6

EXAMPLE

Diagonals (beginning on row 0): {1}; {1,1}; {1,2,1}; {1,1,1,1}; {1,2,2,2,1}; ...

CROSSREFS

T(n, n)=A002420, T(n, n+1)=A000108 (Catalan numbers).

The following are all versions of (essentially) the same Catalan triangle: A009766, A030237, A033184, A059365, A099039, A106566, A130020, A047072.

Diagonals give A000108 A000245 A002057 A000344 A003517 A000588 A003518 A003519 A001392, ...

Sequence in context: A245618 A228053 A031262 * A178058 A260971 A053258

Adjacent sequences:  A047069 A047070 A047071 * A047073 A047074 A047075

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling

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 December 15 03:08 EST 2017. Contains 296020 sequences.