A291337 p-INVERT of (1,1,1,1,1,...), where p(S) = 1 - 2 S - 2 S^3.
1, 3, 10, 34, 115, 387, 1300, 4366, 14665, 49263, 165490, 555934, 1867555, 6273687, 21075220, 70798066, 237832225, 798950763, 2683918570, 9016098634, 30287816995, 101745987387, 341795711140, 1148195728966, 3857138603785, 12957301471863, 43527515777650
Offset: 0
Links
- Clark Kimberling, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (5,-7,5).
Programs
-
Magma
R
:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1-2*x+2*x^2)/(1-5*x+7*x^2-5*x^3) )); // G. C. Greubel, Jun 01 2023 -
Mathematica
z = 60; s = 1 - 2 s - 2 s^3; Drop[CoefficientList[Series[s, {x, 0, z}], x], 1] (* A000012 *) u = Drop[CoefficientList[Series[1/p, {x, 0, z}], x], 1] (* A291005 *) u / 2 (* A291337 *) -
SageMath
def A291337_list(prec): P.
= PowerSeriesRing(ZZ, prec) return P( (1-2*x+2*x^2)/(1-5*x+7*x^2-5*x^3) ).list() A291337_list(30) # G. C. Greubel, Jun 01 2023
Formula
G.f.: (1 - 2*x + 2*x^2)/(1 - 5*x + 7*x^2 - 5*x^3).
a(n) = 5*a(n-1) - 7*a(n-2) + 5*a(n-3) for n >= 4.
a(n) = (1/2)*A291005(n).