A245437 Expansion of x^5/(x^6-x^4-x^2-x+1).

0, 0, 0, 0, 0, 1, 1, 2, 3, 6, 10, 17, 29, 50, 86, 147, 252, 432, 741, 1270, 2177, 3732, 6398, 10968, 18802, 32232, 55255, 94723, 162382, 278369, 477204, 818064, 1402395, 2404105, 4121322, 7065122, 12111635, 20762798, 35593360, 61017175, 104600848, 179315699

Offset

0,8

Comments

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Srecko Brlek, Andrea Frosini, Simone Rinaldi, Laurent Vuillon, Tilings by translation: enumeration by a rational language approach, The Electronic Journal of Combinatorics, vol. 13 (2006).

Index entries for linear recurrences with constant coefficients, signature (1,1,0,1,0,-1).

Formula

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

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

Mathematica

CoefficientList[Series[x^5/(x^6 - x^4 - x^2 - x + 1), {x, 0, 50}], x]
LinearRecurrence[{1, 1, 0, 1, 0, -1}, {0, 0, 0, 0, 0, 1}, 50] (* Bruno Berselli, Jul 22 2014 *)

Prog

(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]];

Crossrefs

Cf. A079500, A175331, A244521, A245185.

Sequence in context: A324015 A238777 A344615 * A285665 A135431 A123908

Adjacent sequences: A245434 A245435 A245436 * A245438 A245439 A245440

Keyword

nonn,easy

Author

Vincenzo Librandi, Jul 22 2014

Status

approved