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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A191684 Number of lattice paths from (0,0) to (n,n) using steps (0,1), (0,2), (1,0), (2,2). 1
1, 2, 10, 46, 233, 1196, 6274, 33292, 178378, 962616, 5224965, 28494124, 156000816, 856903772, 4720235840, 26064910068, 144236627991, 799671246842, 4440913771641, 24699098156578, 137553727513369, 766990846033320, 4281404671954689, 23923170440346544 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

FORMULA

G.f.: A(x) where (4*x^6-13*x^4-18*x^3+41*x^2+22*x-5)*A(x)^3+(4-3*x^2)*A(x)+1=0. - Mark van Hoeij, Apr 17 2013

MAPLE

P := (4*x^6-13*x^4-18*x^3+41*x^2+22*x-5)*A^3+(4-3*x^2)*A+1;

series(RootOf(P, A), x=0, 30); # Mark van Hoeij, Apr 17 2013

# second Maple program:

b:= proc(p) b(p):= `if`(p=[0$2], 1, `if`(min(p[])<0, 0,

      add(b(p-l), l=[[0, 1], [0, 2], [1, 0], [2, 2]])))

    end:

a:= n-> b([n$2]):

seq(a(n), n=0..30);  # Alois P. Heinz, Aug 18 2014

MATHEMATICA

b[p_List] := b[p] = If[p == {0, 0}, 1, If[Min[p] < 0, 0, Sum[b[p-l], {l, {{0, 1}, {0, 2}, {1, 0}, {2, 2}}}]]]; a[n_] := b[{n, n}]; Table[a[n], {n, 0, 30}] (* Jean-Fran├žois Alcover, May 27 2015, after Alois P. Heinz *)

PROG

(PARI) /* same as in A092566 but use */

steps=[[0, 1], [0, 2], [1, 0], [2, 2]];

/* Joerg Arndt, Jun 30 2011 */

CROSSREFS

Sequence in context: A029706 A191644 A009640 * A081167 A321274 A166107

Adjacent sequences:  A191681 A191682 A191683 * A191685 A191686 A191687

KEYWORD

nonn

AUTHOR

Joerg Arndt, Jun 30 2011

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 October 17 14:39 EDT 2019. Contains 328114 sequences. (Running on oeis4.)