A141325 a(n) = A000045(n) + A131531(n+3).

1, 1, 1, 1, 3, 5, 9, 13, 21, 33, 55, 89, 145, 233, 377, 609, 987, 1597, 2585, 4181, 6765, 10945, 17711, 28657, 46369, 75025, 121393, 196417, 317811, 514229, 832041, 1346269, 2178309, 3524577, 5702887, 9227465, 14930353, 24157817, 39088169

Offset

0,5

Links

Michael De Vlieger, Table of n, a(n) for n = 0..4786

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

Formula

G.f.: (1-x^2+x^4)/((1+x)*(1-x+x^2)*(1-x-x^2)). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 12 2009

Mathematica

LinearRecurrence[{1, 1, -1, 1, 1}, {1, 1, 1, 1, 3}, 40] (* Jean-François Alcover, Aug 16 2017 *)
Table[Fibonacci@ n + Boole[Mod[n, 3] == 0] - 2 Boole[Mod[n, 6] == 3], {n, 0, 40}] (* Michael De Vlieger, Aug 16 2017 *)

Prog

(PARI) my(x='x+O('x^40)); Vec((1-x^2+x^4)/((1+x^3)*(1-x-x^2))) \\ G. C. Greubel, Jun 11 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1-x^2+x^4)/((1+x^3)*(1-x-x^2)) )); // G. C. Greubel, Jun 11 2019
(Sage) ((1-x^2+x^4)/((1+x^3)*(1-x-x^2))).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Jun 11 2019

Crossrefs

Cf. A014437, A140096, A140413.

Sequence in context: A136252 A354788 A187212 * A248604 A146905 A052282

Adjacent sequences: A141322 A141323 A141324 * A141326 A141327 A141328

Keyword

nonn,easy

Author

Paul Curtz, Aug 03 2008

Extensions

Definition corrected by R. J. Mathar, Sep 16 2009

More terms from R. J. Mathar, Sep 27 2009

Status

approved