A074678 a(n) = Sum_{j=0..floor(n/2)} (-1)^(j+floor(n/2))*S(2j+q), where S(n) are generalized tribonacci numbers (A001644) and q = (1-(-1)^n)/2.

3, 1, 0, 6, 11, 15, 28, 56, 103, 185, 340, 630, 1159, 2127, 3912, 7200, 13243, 24353, 44792, 82390, 151539, 278719, 512644, 942904, 1734271, 3189817, 5866988, 10791078, 19847887, 36505951, 67144912, 123498752, 227149619, 417793281

Offset

0,1

Comments

a(n) is the convolution of S(n) with the sequence (1,0,-1,0,1,0,-1,0,....) A056594.

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) = Sum_{j=0..floor(n/2)} (-1)^(j+floor(n/2))*S(2j+q), where S(n) are generalized tribonacci numbers (A001644) and q = (1-(-1)^n)/2.

a(n) = a(n-1) + 2*a(n-3) + a(n-4) + a(n-5), a(0)=3, a(1)=1, a(2)=0, a(3)=6, a(4)=11.

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, 40}], x]
LinearRecurrence[{1, 0, 2, 1, 1}, {3, 1, 0, 6, 11}, 40] (* G. C. Greubel, Apr 02 2019 *)

Prog

(PARI) my(x='x+O('x^40)); Vec((3-2*x-x^2)/(1-x-2*x^3-x^4-x^5)) \\ G. C. Greubel, Apr 02 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (3-2*x-x^2)/(1-x-2*x^3-x^4-x^5) )); // G. C. Greubel, Apr 02 2019
(Sage) ((3-2*x-x^2)/(1-x-2*x^3-x^4-x^5)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Apr 02 2019
(GAP) a:=[3, 1, 0, 6, 11];; for n in [6..40] do a[n]:=a[n-1]+2*a[n-3]+a[n-4] +a[n-5]; od; a; # G. C. Greubel, Apr 02 2019

Crossrefs

Cf. A001644, A056594.

Sequence in context: A248826 A058152 A058140 * A363976 A201586 A130888

Adjacent sequences: A074675 A074676 A074677 * A074679 A074680 A074681

Keyword

easy,nonn

Author

Mario Catalani (mario.catalani(AT)unito.it), Aug 30 2002

Status

approved