A106691 Expansion of g.f. (1+x-2*x^2+x^3+x^4)/((1-x)^2*(1+x)^2*(1+2*x)^2).

1, -3, 8, -17, 36, -71, 140, -269, 516, -979, 1852, -3481, 6516, -12127, 22444, -41253, 75236, -135915, 242716, -427185, 737876, -1242743, 2019468, -3106877, 4349636, -4971011, 2485500, 9942071, -49710284, 159072881, -437450388, 1113510059, -2704238684, 6362914533, -14634703396

Offset: 0

Author

Creighton Dement, May 13 2005

Keywords

• sign
• easy

Comments

Floretion Algebra Multiplication Program, FAMP Code: 2jbasekrokseq[ - .25'i - .25i' + 'ii' + .25'jk' + .25'kj'], RokType: Y[sqa.Findk()] = Y[sqa.Findk()] - p (internal program code)

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-4,-2,8,7,-4,-4).

Crossrefs

Cf. A002697.

Programs

Magma

[(1/54)*(3*n +4 -27*(-1)^n*(n+4) +(-2)^(n+1)*(3*n-79)): n in [0..40]]; // G. C. Greubel, Sep 09 2021

Mathematica

CoefficientList[Series[(1+x-2x^2+x^3+x^4)/((1-x)^2(1+x)^2(1+2x)^2),{x,0,40}],x] (* or *) LinearRecurrence[{-4,-2,8,7,-4,-4},{1,-3,8,-17,36,-71},40] (* Harvey P. Dale, Dec 21 2015 *)

SageMath

[(1/54)*(3*n +4 -27*(-1)^n*(n+4) +(-2)^(n+1)*(3*n-79)) for n in (0..40)] # G. C. Greubel, Sep 09 2021

Formula

From G. C. Greubel, Sep 09 2021: (Start)

a(n) = (1/54)*(3*n +4 -27*(-1)^n*(n+4) +(-2)^(n+1)*(3*n-79)).

E.g.f.: (1/54)*((4 +3*x)*exp(x) -27*(4 -x)*exp(-x) + 2*(79 +6*x)*exp(-2*x)). (End)