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 A051436 Number of undirected walks of length n+1 on tetrahedron, visiting n+2 vertices, with n "corners", as in A001998, but allowing only rigid motions in 3-space (|G| = 12). Walks are not self-avoiding. 2
 1, 2, 5, 12, 39, 111, 350, 1044, 3201, 9627, 29150, 87672, 264069, 793431, 2384450, 7159164, 21494001, 64507827, 193589270, 580878432, 1742897949, 5229157551, 15688522250, 47067483684, 141206647401, 423627793227, 1270900160990, 3812732430792, 11438264409429 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (5,0,-30,25,55,-60,-30,36). FORMULA n=2m: (3^n+3^m)/2 -2^(n-1)+2^(m-1); n=2m+1: (3^n+3^m)/2 - 2^(n-1) +1. G.f.: -(39*x^7-20*x^6-39*x^5+14*x^4+17*x^3-5*x^2-3*x+1) / ((x-1)*(x+1)*(2*x-1)*(3*x-1)*(2*x^2-1)*(3*x^2-1)). - Colin Barker, Jul 17 2013 EXAMPLE For n=2 there are three walks that stay in one face and two that visit two faces. MAPLE a:= n-> `if`(irem(n, 2, 'm')=0,         (3^n+3^m)/2+2^(m-1), (3^n+3^m)/2+1) -2^(n-1): seq(a(n), n=0..35);  # Alois P. Heinz, Jul 17 2013 MATHEMATICA a[n_?OddQ] := (3^n + 3^((n - 1)/2))/2 - 2^(n - 1) + 1; a[n_?EvenQ] := (3^n + 3^(n/2))/2 - 2^(n - 1) + 2^(n/2 - 1); Table[a[n], {n, 0, 22}] (* Jean-François Alcover, Jan 25 2013, from formula *) LinearRecurrence[{5, 0, -30, 25, 55, -60, -30, 36}, {1, 2, 5, 12, 39, 111, 350, 1044}, 40] (* Harvey P. Dale, Oct 30 2015 *) PROG (Haskell) a051436 n = (3 ^ n + 3 ^ m - 2 ^ n + (1 - r) * 2 ^ m) `div` 2 + r             where (m, r) = divMod n 2 -- Reinhard Zumkeller, Jun 30 2013 (PARI) a(n)=if(n%2, (3^n + 3^((n - 1)/2))/2 + 1, (3^n + 3^(n/2))/2 + 2^(n/2 - 1)) - 2^(n-1) \\ Charles R Greathouse IV, Feb 10 2017 CROSSREFS Cf. A001998, A001444, A000079, A000244. Sequence in context: A036782 A050237 A050258 * A054581 A203151 A140440 Adjacent sequences:  A051433 A051434 A051435 * A051437 A051438 A051439 KEYWORD nonn,walk,nice,easy AUTHOR EXTENSIONS Corrected by T. D. Noe, Nov 09 2006 STATUS approved

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Last modified August 18 06:41 EDT 2018. Contains 313823 sequences. (Running on oeis4.)