A217733 Expansion of (1+x-x^2)/((1-x)*(1-3*x^2-x^3)).

1, 2, 4, 8, 15, 29, 54, 103, 192, 364, 680, 1285, 2405, 4536, 8501, 16014, 30040, 56544, 106135, 199673, 374950, 705155, 1324524, 2490416, 4678728, 8795773, 16526601, 31066048, 58375577, 109724746, 206192780, 387549816, 728303087, 1368842229, 2572459078, 4834829775, 9086219464

Offset: 0

Author

Philippe Deléham, Mar 22 2013

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (1,3,-2,-1).

Crossrefs

Cf. A065455, A216236.

Programs

Magma

m:=40; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((1+x-x^2)/((1-x)*(1-3*x^2-x^3)))); // Bruno Berselli, Mar 25 2013

Mathematica

CoefficientList[Series[(1 + x - x^2)/((1 - x) (1 - 3 x^2 - x^3)), {x, 0, 40}], x] (* Bruno Berselli, Mar 25 2013 *)

Maxima

makelist(coeff(taylor((1+x-x^2)/((1-x)*(1-3*x^2-x^3)), x, 0, n), x, n), n, 0, 40); /* Bruno Berselli, Mar 25 2013 */

Formula

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

a(n) = sum( A216236(n-k,k), 0<=k<=n ).

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

a(n+1) - a(n) = A065455(n).