A239909 Arises from a construction of equiangular lines in complex space of dimension 2.

1, 1, 2, 3, 5, 9, 15, 26, 45, 77, 133, 229, 394, 679, 1169, 2013, 3467, 5970, 10281, 17705, 30489, 52505, 90418, 155707, 268141, 461761, 795191, 1369386, 2358197, 4061013, 6993405, 12043229, 20739450, 35715071, 61504345, 105915637, 182395603, 314100514

Offset

1,3

Comments

a(n+2) is the number of binary words of length n in which every run of zeros has length congruent to 1 modulo 3. - Ira M. Gessel, Jan 22 2025

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

G. McConnell, Some non-standard ways to generate SIC-POVMs in dimensions 2 and 3, arXiiv preprint arXiv:1402.7330, 2014, p. 4.

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

Formula

From Vincenzo Librandi Apr 09 2014: (Start)

G.f.: x*(1-x^3)/(x^4-x^3-x^2-x+1).

a(n) = a(n-1) + a(n-2) + a(n-3) - a(n-4) for n>4.

a(n) = a(n-1) + 2*a(n-3) + A116732(n-5) for n>4. (End)

Mathematica

LinearRecurrence[{1, 1, 1, -1}, {1, 1, 2, 3}, 40] (* or *) CoefficientList[Series[(1 - x^3)/(x^4 - x^3 - x^2 - x + 1), {x, 0, 100}], x] (* Vincenzo Librandi, Apr 09 2014 *)

Prog

(Magma) I:=[1, 1, 2, 3]; [n le 4 select I[n] else Self(n-1)+Self(n-2)+Self(n-3)-Self(n-4): n in [1..50]];

Crossrefs

Cf. A116732.

Sequence in context: A018157 A228644 A003065 * A185648 A228645 A185649

Adjacent sequences: A239906 A239907 A239908 * A239910 A239911 A239912

Keyword

nonn,easy

Author

N. J. A. Sloane, Apr 09 2014

Status

approved