login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A284414 Number T(n,k) of self-avoiding planar walks of length k starting at (0,0), ending at (n,0), remaining in the first quadrant and using steps (0,1), (1,0), (1,1), (-1,1), and (1,-1) with the restriction that (0,1) is never used below the diagonal and (1,0) is never used above the diagonal; triangle T(n,k), n>=0, n<=k<=n*(n+3)/2, read by rows. 10
1, 1, 1, 2, 1, 1, 1, 4, 4, 4, 7, 3, 1, 1, 9, 8, 16, 21, 17, 15, 10, 9, 4, 1, 1, 21, 22, 54, 87, 87, 116, 99, 91, 78, 42, 31, 17, 10, 5, 1, 1, 51, 54, 178, 269, 370, 499, 536, 590, 560, 510, 420, 350, 268, 185, 132, 69, 44, 23, 11, 6, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Alois P. Heinz, Rows n = 0..50, flattened

Alois P. Heinz, Animation of T(5,12)=91 walks

Wikipedia, Lattice_path

Wikipedia, Self-avoiding walk

FORMULA

Sum_{k=n..n*(n+3)/2} (k+1) * T(n,k) = A284231(n).

EXAMPLE

Triangle T(n,k) begins:

1;

.  1, 1;

.  .  2, 1, 1,  1;

.  .  .  4, 4,  4,  7,  3,  1,  1;

.  .  .  .  9,  8, 16, 21, 17, 15,  10,  9,  4,  1,  1;

.  .  .  .  .  21, 22, 54, 87, 87, 116, 99, 91, 78, 42, 31, 17, 10, 5, 1, 1;

CROSSREFS

Row sums give A284230.

Column sums give A284415.

Antidiagonal sums give A284428.

T(n,n) gives A001006.

T(n,n+1) gives A284778.

T(n,2n) gives A284416.

T(n,n*(n+1)/2) gives A284418.

Cf. A000096, A284231, A284461, A284652 (this triangle read by columns).

Sequence in context: A213268 A291118 A245184 * A140274 A095231 A303697

Adjacent sequences:  A284411 A284412 A284413 * A284415 A284416 A284417

KEYWORD

nonn,tabf,walk

AUTHOR

Alois P. Heinz, Mar 26 2017

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 12 23:19 EDT 2020. Contains 336440 sequences. (Running on oeis4.)