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

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A202411 Sum_{k=floor(n/4)..R} C(k,m*k-(-1)^n*(R-k))*C(k+1,m*(k+2)-(-1)^n*(R-k+1)) where m = (n+1) mod 2 and R = (n+m-3)/2 for n>0 and a(0)=1. 5
 1, 0, 1, 1, 1, 2, 3, 4, 7, 10, 16, 24, 39, 58, 95, 143, 233, 354, 577, 881, 1436, 2204, 3590, 5534, 9011, 13940, 22691, 35213, 57299, 89162, 145043, 226238, 367931, 575114, 935078, 1464382, 2380405, 3734150, 6068745, 9534594, 15492702, 24374230, 39598631 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 LINKS Peter Luschny, Fibonacci meanders. FORMULA For n>0 let H=floor(n/2), A=floor(H/2), R=H-1, B=A-R/2+1, C=A+1, D=A-R, J=n mod 2 and Z = if(H mod 2 = 1,(H+1)/2,H^2*(H+2)/16) if J = 0 else Z = if(H mod 2 = 1,1, H*(H+2)/4). Then a(n) = Z*Hypergeometric([1,C,C+1,D,D-J],[B,B,B-1/2,B+1/2-J],1/16). EXAMPLE Fibonacci meanders classified by maximal run length of 1s (see the link) lead to the triangle 0,1; 1,1,0,1; 2,1,1,1,0,1; 4,3,2,1,1,1,0,1; 10,7,4,3,2,1,1,1,0,1; 24,16,10,7,4,3,2,1,1,1,0,1. MAPLE A202411 := proc(n) local A, R, B, C, D, Z, H, J; if n = 0 then RETURN(1) fi; H:=iquo(n, 2); A:=iquo(H, 2); R:=H-1; B:=A-R/2+1; C:=A+1; D:=A-R; J:=n mod 2; if J = 0 then Z:=`if`(H mod 2 = 1, (H+1)/2, H^2*(H+2)/16) else Z:=`if`(H mod 2 = 1, 1, H*(H+2)/4) fi; Z*hypergeom([1, C, C+1, D, D-J], [B, B, B-1/2, B+1/2-J], 1/16) end: seq(simplify(A202411(i)), i=0..42); MATHEMATICA a[0] = 1; a[n_] := Module[{A, R, B, C, D, Z, H, J}, H = Quotient[n, 2]; A = Quotient[H, 2]; R = H-1; B = A-R/2+1; C = A+1; D = A-R; J = Mod[n, 2]; If[J == 0, Z = If[Mod[H, 2] == 1, (H+1)/2, H^2*(H+2)/16], Z = If[Mod[H, 2] == 1, 1, H*(H+2)/4]]; Z*HypergeometricPFQ[{1, C, C+1, D, D-J}, {B, B, B-1/2, B+1/2-J}, 1/16]]; Table[a[n], {n, 0, 42}] (* Jean-François Alcover, Jan 27 2014, translated from Maple *) CROSSREFS Cf. A110236, A203611. Sequence in context: A159288 A033320 A013982 * A293161 A235648 A051449 Adjacent sequences:  A202408 A202409 A202410 * A202412 A202413 A202414 KEYWORD nonn AUTHOR Peter Luschny, Jan 14 2012 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.

Last modified January 18 16:27 EST 2020. Contains 331011 sequences. (Running on oeis4.)