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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A071201 Array A(n,k) read by antidiagonals giving number of paths up and right from (0,0) to (n,k) where x/y<=n/k. 6
1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 3, 5, 3, 1, 1, 3, 5, 5, 3, 1, 1, 4, 7, 14, 7, 4, 1, 1, 4, 12, 14, 14, 12, 4, 1, 1, 5, 12, 23, 42, 23, 12, 5, 1, 1, 5, 15, 30, 42, 42, 30, 15, 5, 1, 1, 6, 22, 55, 66, 132, 66, 55, 22, 6, 1, 1, 6, 22, 55, 99, 132, 132, 99, 55, 22, 6, 1, 1, 7, 26, 76, 143, 227, 429, 227, 143, 76, 26, 7, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

Alois P. Heinz, Antidiagonals n = 1..141, flattened

Jean-Christophe Aval, François Bergeron, Interlaced rectangular parking functions, arXiv:1503.03991 [math.CO], 2015.

FORMULA

Some identities: A(n,k) = A(k,n); A(n,m*n) = A(n,m*n+1); A(n,n) = A000108(n); if n and k are coprime then A(n,k) = A071202(n,k).

Sum_{k=1..n-1} A(n-k,k) = A298072(n)-2 for n>0. - Lee A. Newberg, Jan 18 2018

EXAMPLE

Table starts:

1, 1, 1,  1,  1,  1, ...

1, 2, 2,  3,  3,  4, ...

1, 2, 5,  5,  7, 12, ...

1, 3, 5, 14, 14, 23, ...

1, 3, 7, 14, 42, 42, ...

...

MAPLE

b:= proc(x, y, r) option remember; `if`(y<0 or y>x*r, 0,

      `if`(x=0, 1, b(x-1, y, r) +b(x, y-1, r)))

    end:

A:= (n, k)-> `if`(k<n, b(k, n, n/k), b(n, k, k/n)):

seq(seq(A(n, 1+d-n), n=1..d), d=1..14);  # Alois P. Heinz, Mar 20 2015

MATHEMATICA

b[x_, y_, r_] := b[x, y, r] = If[y < 0 || y > x*r, 0, If[x == 0, 1, b[x - 1, y, r] + b[x, y - 1, r]]]; A[n_, k_] := If[k < n, b[k, n, n/k], b[n, k, k/n]]; Table[Table[A[n, 1 + d - n], {n, 1, d}], {d, 1, 14}] // Flatten (* Jean-François Alcover, Jan 30 2016, after Alois P. Heinz *)

CROSSREFS

Cf. A260419, A298072.

Sequence in context: A090806 A241926 A174446 * A240656 A106476 A101566

Adjacent sequences:  A071198 A071199 A071200 * A071202 A071203 A071204

KEYWORD

nonn,tabl

AUTHOR

Henry Bottomley, May 16 2002

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 18 05:48 EST 2018. Contains 299298 sequences. (Running on oeis4.)