OFFSET
1,4
COMMENTS
Also (essentially), coordination sequence for (2,4,infinity) tiling of hyperbolic plane. - N. J. A. Sloane, Dec 29 2015
Column sums of shifted (1,2) Pascal array:
1 1 1 1 1 1 1 1 1
......2 3 4 5 6 7
............2 5 9
.................
----------------- +
1 1 1 3 4 5 8 ...
a(n+1) is the number of multus bitstrings of length n with no runs of 2 0's. - Steven Finch, Mar 25 2020
From Areebah Mahdia and Greg Dresden, Jun 13 2020: (Start)
For n >= 5, a(n) gives the number of ways to tile the following board of length n-3 with squares and trominos:
._ _
|_|_|
|_|_|_ _ _ _ _
|_|_|_|_|_|_|_| ... . (End)
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
J. W. Cannon, P. Wagreich, Growth functions of surface groups, Mathematische Annalen, 1992, Volume 293, pp. 239-257. See Prop. 3.1.
Steven Finch, Cantor-solus and Cantor-multus distributions, arXiv:2003.09458 [math.CO], 2020.
Index entries for linear recurrences with constant coefficients, signature (1,0,1).
FORMULA
G.f.: x - x^2*(1+2*x^2) / ( -1+x+x^3 ). - R. J. Mathar, Oct 30 2011
MATHEMATICA
Join[{1}, LinearRecurrence[{1, 0, 1}, {1, 1, 3}, 80]] (* Vladimir Joseph Stephan Orlovsky, Feb 15 2012 *)
PROG
(Haskell)
a179070 n = a179070_list !! (n-1)
a179070_list = 1 : zs where zs = 1 : 1 : 3 : zipWith (+) zs (drop 2 zs)
-- Reinhard Zumkeller, Jul 23 2012
(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
CROSSREFS
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.
KEYWORD
easy,nonn
AUTHOR
Mark Dols, Jun 27 2010
EXTENSIONS
Simpler definition from N. J. A. Sloane, Aug 29 2013
STATUS
approved