A073748 a(n) = S(n)*S(n-1), where S(n) are the generalized tribonacci numbers A001644.

-3, 3, 3, 21, 77, 231, 819, 2769, 9301, 31571, 106763, 361045, 1221685, 4132743, 13980747, 47297217, 160004685, 541291715, 1831178355, 6194830005, 20956959933, 70896891079, 239842458947, 811381229009, 2744883043045, 9285872805715, 31413882695739, 106272403946805

Offset: 0

Author

Maio Catalani (mario.catalani(AT)unito.it), Aug 08 2002

Keywords

• easy
• sign

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2, 3, 6, -1, 0, -1).

Crossrefs

Cf. A001644, A073145.

Programs

Magma

R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (-3+9*x+6*x^2+24*x^3+5*x^4-x^5)/(1-2*x-3*x^2-6*x^3 +x^4+x^6) )); // G. C. Greubel, Apr 21 2019

Mathematica

CoefficientList[Series[(-3+9*x+6*x^2+24*x^3+5*x^4-x^5)/(1-2*x-3*x^2-6*x^3 +x^4+x^6), {x, 0, 30}], x]
Join[{-3},Times@@@Partition[LinearRecurrence[{1,1,1},{3,1,3},30],2,1]] (* or *) LinearRecurrence[{2,3,6,-1,0,-1},{-3,3,3,21,77,231},30] (* Harvey P. Dale, Nov 18 2013 *)

PARI

my(x='x+O('x^30)); Vec((-3+9*x+6*x^2+24*x^3+5*x^4-x^5)/(1-2*x-3*x^2-6*x^3 +x^4+x^6)) \\ G. C. Greubel, Apr 21 2019

Sage

((-3+9*x+6*x^2+24*x^3+5*x^4-x^5)/(1-2*x-3*x^2-6*x^3 +x^4+x^6)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Apr 21 2019

Formula

a(n) = S(2*n-1) + C(n-1) - C(n-2), where S(n) is A001644, C(n) is A073145.

G.f.: (-3 + 9*x + 6*x^2 + 24*x^3 + 5*x^4 - x^5)/(1 - 2*x - 3*x^2 - 6*x^3 + x^4 + x^6).

a(0)=-3, a(1)=3, a(2)=3, a(3)=21, a(4)=77, a(5)=231, a(n) = 2*a(n-1) + 3*a(n-2) + 6*a(n-3) - a(n-4) - a(n-6). - Harvey P. Dale, Nov 18 2013