A074475 a(n) = Sum_{j=0..floor(n/2)} T(2*j + q), where T(n) are generalized tribonacci numbers (A001644) and q = n - 2*floor(n/2).

3, 1, 6, 8, 17, 29, 56, 100, 187, 341, 630, 1156, 2129, 3913, 7200, 13240, 24355, 44793, 82390, 151536, 278721, 512645, 942904, 1734268, 3189819, 5866989, 10791078, 19847884, 36505953, 67144913, 123498752, 227149616, 417793283

Offset: 0

Author

Mario Catalani (mario.catalani(AT)unito.it), Aug 23 2002

Keywords

• easy
• nonn

Comments

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

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,2,2,1).

Crossrefs

Cf. A001644, A074331.

Programs

Magma

R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (3+x)/(1-2*x^2-2*x^3-x^4) )); // G. C. Greubel, Apr 21 2019

Mathematica

CoefficientList[Series[(3+x)/(1-2*x^2-2*x^3-x^4), {x, 0, 40}], x]
LinearRecurrence[{0,2,2,1},{3,1,6,8},40] (* Harvey P. Dale, Jul 08 2017 *)

PARI

my(x='x+O('x^40)); Vec((3+x)/(1-2*x^2-2*x^3-x^4)) \\ G. C. Greubel, Apr 21 2019

Sage

((3+x)/(1-2*x^2-2*x^3-x^4)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Apr 21 2019

Formula

a(n) = 2*a(n-2) + 2*a(n-3) + a(n-4), a(0)=3, a(1)=1, a(2)=6, a(3)=8.

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