A245437 - OEIS

%I #17 Sep 08 2022 08:46:08

%S 0,0,0,0,0,1,1,2,3,6,10,17,29,50,86,147,252,432,741,1270,2177,3732,

%T 6398,10968,18802,32232,55255,94723,162382,278369,477204,818064,

%U 1402395,2404105,4121322,7065122,12111635,20762798,35593360,61017175,104600848,179315699

%N Expansion of x^5/(x^6-x^4-x^2-x+1).

%C G.f. taken from p. 12 of the Brlek et al. reference.

%H Vincenzo Librandi, <a href="/A245437/b245437.txt">Table of n, a(n) for n = 0..1000</a>

%H Srecko Brlek, Andrea Frosini, Simone Rinaldi, Laurent Vuillon, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v13i1r15">Tilings by translation: enumeration by a rational language approach</a>, The Electronic Journal of Combinatorics, vol. 13 (2006).

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,1,0,-1).

%F G.f.: x^5/(x^6 - x^4 - x^2 - x + 1).

%F a(n) = a(n-1) + a(n-2) + a(n-4) - a(n-6) for n>5.

%t CoefficientList[Series[x^5/(x^6 - x^4 - x^2 - x + 1), {x, 0, 50}], x]

%t LinearRecurrence[{1, 1, 0, 1, 0, -1}, {0, 0, 0, 0, 0, 1}, 50] (* _Bruno Berselli_, Jul 22 2014 *)

%o (Magma) [n le 6 select Floor(n/6) else Self(n-1)+Self(n-2)+Self(n-4)-Self(n-6): n in [1..50]];

%Y Cf. A079500, A175331, A244521, A245185.

%K nonn,easy

%O 0,8

%A _Vincenzo Librandi_, Jul 22 2014