A074585 a(n)= Sum_{j=0..floor(n/2)} A073145(2*j + q), where q = 2*(n/2 - floor(n/2)).

3, -1, 2, 4, -3, 3, 8, -12, 11, 11, -30, 32, 13, -73, 96, -8, -157, 263, -110, -308, 685, -485, -504, 1676, -1653, -525, 3858, -4984, 605, 8239, -13824, 6192, 15875, -35889, 26210, 25556, -87651, 88307, 24904, -200860, 264267, -38501, -426622

Offset

0,1

Comments

a(n) is the convolution of A073145(n) with the sequence (1,0,1,0,1,0, ...).

a(n) is also the sum of the reflected (see A074058) sequence of the generalized tribonacci sequence (A001644).

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (-1,0,2,1,-1).

Formula

a(n) = -a(n-1) + 2*a(n-3) + a(n-4) - a(n-5), a(0) = 3, a(1) = -1, a(2) = 2, a(3) = 4, a(4) = -3.

G.f.: (3 + 2*x + x^2)/(1 + x - 2*x^3 - x^4 + x^5).

Mathematica

CoefficientList[ Series[(3+2*x+x^2)/(1+x-2*x^3-x^4+x^5), {x, 0, 50}], x]

Prog

(PARI) my(x='x+O('x^50)); Vec((3+2*x+x^2)/(1+x-2*x^3-x^4+x^5)) \\ G. C. Greubel, Apr 13 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( (3+2*x+x^2)/(1+x-2*x^3-x^4+x^5) )); // G. C. Greubel, Apr 13 2019
(Sage) ((3+2*x+x^2)/(1+x-2*x^3-x^4+x^5)).series(x, 50).coefficients(x, sparse=False) # G. C. Greubel, Apr 13 2019

Crossrefs

Cf. A073145, A074058, A001644, A074331, A074392, A074475.

Sequence in context: A209301 A049992 A227147 * A183312 A108038 A151845

Adjacent sequences: A074582 A074583 A074584 * A074586 A074587 A074588

Keyword

easy,sign

Author

Mario Catalani (mario.catalani(AT)unito.it), Aug 28 2002

Extensions

More terms from Robert G. Wilson v, Aug 29 2002

Status

approved