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 A051437 Number of undirected walks of length n+1 on an oriented triangle, visiting n+2 vertices, with n "corners"; the symmetry group is C3. Walks are not self-avoiding. 6
 1, 3, 4, 10, 16, 36, 64, 136, 256, 528, 1024, 2080, 4096, 8256, 16384, 32896, 65536, 131328, 262144, 524800, 1048576, 2098176, 4194304, 8390656, 16777216, 33558528, 67108864, 134225920, 268435456, 536887296, 1073741824, 2147516416, 4294967296, 8590000128 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS For a way to obtain this sequence from symmetry in quilts, see the Tom Young web page. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 A. Yajima, How to calculate the number of stereoisomers of inositol-homologs, Bull. Chem. Soc. Jpn. 2014, 87, 1260-1264 | doi:10.1246/bcsj.20140204. See Tables 1 and 2 (and text). - N. J. A. Sloane, Mar 26 2015 Tom Young, Math Research Quilt Pattern Symmetry Tom Young, Unique symmetrical triangle quilt patterns along the diagonal of an nxn square (An archived copy from the above page) Index entries for linear recurrences with constant coefficients, signature (2, 2, -4). FORMULA n=2m: a(n)=2^(n-1)+2^((n-2)/2); n=2m+1: a(n)=2^(n-1). - [Note: This formula is for starting offset=1.] a(n) = A000079(n) + A077957(n-1). - Antti Karttunen, Dec 29 2013 Binomial transform is 3^n+Pell(n) (A000244(n)+A000129(n)). G.f.: (1+x-4x^2)/((1-2x)(1-2x^2)); a(n)=2^n+2^(n/2)(1-(-1)^n)/(2sqrt(2)). - Paul Barry, Apr 28 2004 a(0)=1, a(1)=3, a(2)=4, a(n)=2*a(n-1)+2*a(n-2)-4*a(n-3). - Harvey P. Dale, Jun 06 2011 EXAMPLE For n=3 the walks visit vertices 1212, 1213, 1232, 1231. MATHEMATICA LinearRecurrence[{2, 2, -4}, {1, 3, 4}, 50] (* or *) CoefficientList[ Series[ (1+x-4x^2)/((1-2x)(1-2x^2)), {x, 0, 50}], x] (* Harvey P. Dale, Jun 06 2011 *) PROG (Scheme) (define (A051437 n) (if (zero? n) 1 (+ (A000079 n) (A077957 (- n 1))))) ;; Antti Karttunen, Dec 29 2013 CROSSREFS Cf. A000079, A077957, A005418, A193231. Sequence in context: A281903 A093512 A081160 * A224073 A034774 A172416 Adjacent sequences:  A051434 A051435 A051436 * A051438 A051439 A051440 KEYWORD nonn,walk,nice,easy AUTHOR EXTENSIONS More terms from Harvey P. Dale, Jun 06 2011 STATUS approved

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Last modified May 26 21:38 EDT 2018. Contains 304645 sequences. (Running on oeis4.)