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

Author

Paul Curtz, Aug 03 2008

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A014437, A140096, A140413.

Programs

Magma

R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1-x^2+x^4)/((1+x^3)*(1-x-x^2)) )); // G. C. Greubel, Jun 11 2019

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 *)

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

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

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

Extensions

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

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