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

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A026520 a(n) = T(n,n), T given by A026519. Also a(n) = number of integer strings s(0), ..., s(n), counted by T, such that s(n) = 0. 24
1, 1, 2, 4, 8, 20, 38, 104, 196, 556, 1052, 3032, 5774, 16778, 32146, 93872, 180772, 529684, 1024256, 3008864, 5837908, 17184188, 33433996, 98577712, 192239854, 567591142, 1109049320, 3278348608, 6416509142, 18986482250 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
Veronika Irvine, Stephen Melczer, and Frank Ruskey, Vertically constrained Motzkin-like paths inspired by bobbin lace, arXiv:1804.08725 [math.CO], 2018.
FORMULA
a(n) = A026519(n, n).
For n>1, a(n) = 2*A026554(n-1).
MATHEMATICA
T[n_, k_]:= T[n, k]= If[k==0 || k==2*n, 1, If[k==1 || k==2*n-1, Floor[(n+1)/2], If[EvenQ[n], T[n-1, k-2] + T[n-1, k], T[n-1, k-1] + T[n-1, k-2] + T[n-1, k]]]]; (* T = A026519 *)
Table[T[n, n], {n, 0, 40}] (* G. C. Greubel, Dec 19 2021 *)
PROG
(Sage)
@CachedFunction
def T(n, k): # T = A026552
if (k==0 or k==2*n): return 1
elif (k==1 or k==2*n-1): return (n+1)//2
elif (n%2==0): return T(n-1, k) + T(n-1, k-2)
else: return T(n-1, k) + T(n-1, k-1) + T(n-1, k-2)
[T(n, n) for n in (0..40)] # G. C. Greubel, Dec 19 2021
CROSSREFS
Sequence in context: A222562 A252891 A102634 * A282983 A282953 A283047
KEYWORD
nonn
AUTHOR
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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)