The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A047000 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/2 except at the endpoints. 10
 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 3, 2, 1, 1, 1, 4, 5, 2, 2, 1, 1, 5, 9, 7, 4, 3, 1, 1, 6, 14, 16, 7, 3, 4, 1, 1, 7, 20, 30, 23, 7, 7, 5, 1, 1, 8, 27, 50, 53, 30, 14, 12, 6, 1, 1, 9, 35, 77, 103, 83, 30, 12, 18, 7, 1, 1, 10, 44, 112, 180, 186, 113, 30, 30 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS Touches here includes the case where a step touches the line at a midpoint. LINKS Table of n, a(n) for n=0..74. EXAMPLE Diagonals (starting on row #0): {1}; {1,1}; {1,1,1}; {1,2,2,1}; {1,3,2,1,1}; ... T(2,3) = 5; the 5 allowed paths to (2,3) are UUURR, UURUR, UURRU, URUUR, and URURU. PROG (PARI) T(h, k)=if(h==0 || k==0, 1, T(h-1, k)*(h-1!=2*k)+T(h, k-1)*(h!=2*k-2 && h!=2*k-1)) /* Inefficient. */ CROSSREFS The sequence T(2n, n)/2 for n=1, 2, 3, ... is A006013. Sequence in context: A367624 A342748 A117545 * A288915 A175062 A139767 Adjacent sequences: A046997 A046998 A046999 * A047001 A047002 A047003 KEYWORD nonn,tabl AUTHOR Clark Kimberling EXTENSIONS Definition corrected by Franklin T. Adams-Watters, Mar 10 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified March 1 08:46 EST 2024. Contains 370430 sequences. (Running on oeis4.)