A075418 Sum of generalized tribonacci numbers A001644 and inverted tribonacci numbers A075298.

4, 2, -2, 12, 12, 10, 54, 68, 108, 282, 422, 772, 1604, 2674, 5006, 9580, 16884, 31506, 58606, 105948, 196508, 362298, 662022, 1222772, 2249116, 4127210, 7605718, 13984148, 25701652, 47311458, 86994846, 159975004, 294336612, 541281698, 995529822, 1831291692, 3367998380, 6194717674

Offset: 0

Author

Mario Catalani (mario.catalani(AT)unito.it), Sep 14 2002

Keywords

• easy
• sign

Comments

It seems that aside from a(2) the sequence is nonnegative.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0, 1, 4, 1, 0, -1).

Crossrefs

Cf. A001644, A075298.

Programs

Magma

R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (4+2*x-6*x^2-6*x^3+2*x^4+4*x^5)/(1-x^2-4*x^3-x^4+x^6) )); // G. C. Greubel, Apr 21 2019

Mathematica

CoefficientList[Series[(4+2x-6x^2-6x^3+2x^4+4x^5)/(1-x^2-4x^3-x^4+x^6), {x, 0, 40}], x]

PARI

my(x='x+O('x^40)); Vec((4+2*x-6*x^2-6*x^3+2*x^4+4*x^5)/(1-x^2 -4*x^3-x^4+x^6)) \\ G. C. Greubel, Apr 21 2019

Sage

((4+2*x-6*x^2-6*x^3+2*x^4+4*x^5)/(1-x^2-4*x^3-x^4+x^6)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Apr 21 2019

Formula

a(n) = a(n-2) + 4*a(n-3) + a(n-4) - a(n-6), a(0)=4, a(1)=2, a(2)=-2, a(3)=12, a(4)=12, a(5)=10.

O.g.f.: (4 + 2*x - 6*x^2 - 6*x^3 + 2*x^4 + 4*x^5)/(1 - x^2 - 4*x^3 - x^4 + x^6).