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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A302179 The number of 3D walks of length n in an octant returning to axis of origin. 0
 1, 1, 4, 9, 40, 120, 570, 1995, 9898, 38178, 195216, 805266, 4209084, 18239364, 96941130, 436235085, 2349133930, 10891439130, 59272544760, 281544587610, 1545550116240, 7489973640240, 41416083787260, 204122127237210, 1135679731004700, 5678398655023500, 31760915181412800, 160789633105902300 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..27. Nachum Dershowitz, Touchard's Drunkard, Journal of Integer Sequences, Vol. 20 (2017), #17.1.5. The sequence is type aac in Table 3. FORMULA a(n) = Sum_{i=0..n, j=0..n-i, i,j even} A126120(i) * A126120(j) * A001405(n-i-j) * n!/(i! * j! * (n-i-j)!). - Nachum Dershowitz, Aug 06 2020 PROG (PARI) C(n) = binomial(2*n, n)/(n+1); \\ A000108 f(n) = binomial(n, floor(n/2)); \\ A001405 a(n) = sum(i=0, n, if (!(i%2), sum(j=0, n-i, if (!(j%2), C(i/2)*C(j/2)*f(n-i-j)*n!/(i! * j! * (n-i-j)!))))); \\ Michel Marcus, Aug 07 2020 CROSSREFS Cf. A000108, A000984, A002212, A002896, A005572, A026375, A064037, A081671, A138547, A145847, A145867, A150500, A202814. Sequence in context: A149163 A149164 A238420 * A354738 A073414 A085110 Adjacent sequences: A302176 A302177 A302178 * A302180 A302181 A302182 KEYWORD nonn,walk AUTHOR N. J. A. Sloane, Apr 09 2018 EXTENSIONS a(13)-a(27) from Nachum Dershowitz, Aug 04 2020 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 September 28 22:22 EDT 2023. Contains 365739 sequences. (Running on oeis4.)