# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a179070 Showing 1-1 of 1 %I A179070 #49 May 19 2024 13:25:06 %S A179070 1,1,1,3,4,5,8,12,17,25,37,54,79,116,170,249,365,535,784,1149,1684, %T A179070 2468,3617,5301,7769,11386,16687,24456,35842,52529,76985,112827, %U A179070 165356,242341,355168,520524,762865,1118033,1638557,2401422,3519455,5158012,7559434 %N A179070 a(1)=a(2)=a(3)=1, a(4)=3; thereafter a(n) = a(n-1) + a(n-3). %C A179070 Also (essentially), coordination sequence for (2,4,infinity) tiling of hyperbolic plane. - _N. J. A. Sloane_, Dec 29 2015 %C A179070 Column sums of shifted (1,2) Pascal array: %C A179070 1 1 1 1 1 1 1 1 1 %C A179070 ......2 3 4 5 6 7 %C A179070 ............2 5 9 %C A179070 ................. %C A179070 ----------------- + %C A179070 1 1 1 3 4 5 8 ... %C A179070 a(n+1) is the number of multus bitstrings of length n with no runs of 2 0's. - _Steven Finch_, Mar 25 2020 %C A179070 From _Areebah Mahdia_ and _Greg Dresden_, Jun 13 2020: (Start) %C A179070 For n >= 5, a(n) gives the number of ways to tile the following board of length n-3 with squares and trominos: %C A179070 ._ _ %C A179070 |_|_| %C A179070 |_|_|_ _ _ _ _ %C A179070 |_|_|_|_|_|_|_| ... . (End) %H A179070 Reinhard Zumkeller, Table of n, a(n) for n = 1..1000 %H A179070 J. W. Cannon, P. Wagreich, Growth functions of surface groups, Mathematische Annalen, 1992, Volume 293, pp. 239-257. See Prop. 3.1. %H A179070 Steven Finch, Cantor-solus and Cantor-multus distributions, arXiv:2003.09458 [math.CO], 2020. %H A179070 Index entries for linear recurrences with constant coefficients, signature (1,0,1). %F A179070 a(n) = A000930(n-1) + A000930(n-4). %F A179070 G.f.: x - x^2*(1+2*x^2) / ( -1+x+x^3 ). - _R. J. Mathar_, Oct 30 2011 %F A179070 a(n) = A000930(n-2)+2*A000930(n-4) for n>3. - _R. J. Mathar_, May 19 2024 %t A179070 Join[{1}, LinearRecurrence[{1, 0, 1}, {1, 1, 3}, 80]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 15 2012 *) %o A179070 (Haskell) %o A179070 a179070 n = a179070_list !! (n-1) %o A179070 a179070_list = 1 : zs where zs = 1 : 1 : 3 : zipWith (+) zs (drop 2 zs) %o A179070 -- _Reinhard Zumkeller_, Jul 23 2012 %o A179070 (PARI) a(n)=([0,1,0; 0,0,1; 1,0,1]^(n-1)*[1;1;1])[1,1] \\ _Charles R Greathouse IV_, Apr 08 2016 %Y A179070 Cf. A000930, A029635, A097333, A214626. %Y A179070 Coordination sequences for triangular tilings of hyperbolic space: A001630, A007283, A054886, A078042, A096231, A163876, A179070, A265057, A265058, A265059, A265060, A265061, A265062, A265063, A265064, A265065, A265066, A265067, A265068, A265069, A265070, A265071, A265072, A265073, A265074, A265075, A265076, A265077. %K A179070 easy,nonn %O A179070 1,4 %A A179070 _Mark Dols_, Jun 27 2010 %E A179070 Simpler definition from _N. J. A. Sloane_, Aug 29 2013 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE