A238236 Expansion of (1-x-x^2)/((x-1)*(x^3+3*x^2+2*x-1)).

1, 2, 6, 18, 55, 169, 520, 1601, 4930, 15182, 46754, 143983, 443409, 1365520, 4205249, 12950466, 39882198, 122821042, 378239143, 1164823609, 3587185688, 11047081345, 34020543362, 104769516446, 322647744322, 993624581343, 3059961912097, 9423445312544

Offset: 0

Author

Philippe Deléham, Feb 20 2014

Keywords

• nonn
• easy

Comments

Row sums of the triangle in A152440.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (3,1,-2,-1).

Crossrefs

Cf. A097472, A152440, A099098 (first differences).

Programs

Mathematica

CoefficientList[Series[(1 - x - x^2)/(1 - 3 x - x^2 + 2 x^3 + x^4), {x, 0, 40}], x ](* Vincenzo Librandi, Feb 22 2014 *)

Formula

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

a(n) = 3*a(n-1) + a(n-2) -2*a(n-3) - a(n-4), a(0) = 1, a(1) = 2, a(2) = 6, a(3) = 18.

a(n) = A097472(n) - A097472(n-1) - A097472(n-2).

a(n) = A060945(2*n).

a(n)-a(n-1) = A099098(n). - R. J. Mathar, Jun 17 2020