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 A356258 Number of 6-dimensional cubic lattice walks that start and end at origin after 2n steps, free to pass through origin at intermediate stages. 2
 1, 12, 396, 19920, 1281420, 96807312, 8175770064, 748315668672, 72729762868620, 7402621930738320, 781429888276676496, 84955810313787521472, 9463540456205136873936, 1075903653146632508721600, 124461755084172965028753600, 14615050011682746903615601920 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..467 FORMULA E.g.f.: Sum_{n>=0} a(2*n) * x^(2*n)/(2*n)! = I_0(2*x)^6. (I = Modified Bessel function first kind). a(n) = Sum_{h+i+j+k+l+m=n, 0<=h,i,j,k,l,m<=n} multinomial(2n [h,h,i,i,j,j,k,k,l,l,m,m]). - Shel Kaphan, Jan 29 2023 EXAMPLE a(1)=12, because twelve paths start at the origin, visit one of the adjacent vertices, and immediately return to the origin, resulting in 12 different paths of length 2n=2*1=2. MAPLE b:= proc(n, i) option remember; `if`(n=0 or i=1, 1, add(b(n-j, i-1)*binomial(n, j)^2, j=0..n)) end: a:= n-> (2*n)!*b(n, 6)/n!^2: seq(a(n), n=0..15); # Alois P. Heinz, Jan 30 2023 CROSSREFS Row k=6 of A287318. 1-5 dimensional analogs are A000984, A002894, A002896, A039699, A287317. Sequence in context: A138914 A326220 A308129 * A286038 A276482 A202788 Adjacent sequences: A356255 A356256 A356257 * A356259 A356260 A356261 KEYWORD nonn,easy,walk AUTHOR Dave R.M. Langers, Oct 12 2022 STATUS approved

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Last modified September 26 03:54 EDT 2023. Contains 365650 sequences. (Running on oeis4.)