A123957 Expansion of g.f.: x^4/((1+2*x) * (1-2*x+x^2+2*x^3)).

0, 0, 0, 1, 0, 3, -4, 5, -24, 19, -76, 133, -208, 627, -852, 2181, -4232, 7443, -18012, 30533, -66880, 133875, -250724, 547013, -1020152, 2108435, -4245612, 8217861, -17089968, 33202291, -67158900, 135095301, -265925992, 541112339, -1069523580, 2146659781, -4309316128, 8553624307

Offset: 1

Author

Roger L. Bagula and Gary W. Adamson, Oct 27 2006

Keywords

• sign

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (0,3,-4,-4).

Programs

GAP

a:=[0, 0, 0, 1];; for n in [5..40] do a[n]:=3*a[n-2]-4*a[n-3] -4*a[n-4]; od; a; # G. C. Greubel, Aug 05 2019

Magma

R:=PowerSeriesRing(Integers(), 40); [0,0,0] cat Coefficients(R!( x^4/((1+2*x)*(1-2*x+x^2+2*x^3)) )); // G. C. Greubel, Aug 05 2019

Maple

seq(coeff(series(x^4/((1+2*x)*(1-2*x+x^2+2*x^3)), x, n+1), x, n), n = 1..40); # G. C. Greubel, Aug 05 2019

Mathematica

M = {{0,1,0,0}, {0,0,1,0}, {0,0,0,1}, {-4,-4,3,0}}; v[1] = {0,0,0,1}; v[n_]:= v[n] = M.v[n-1]; Table[v[n][[1]], {n, 40}]
Rest@CoefficientList[Series[x^4/((1+2*x)*(1-2*x+x^2+2*x^3)),{x,0,40}],x] (* or *) LinearRecurrence[{0,3,-4,-4},{0,0,0,1},40] (* Harvey P. Dale, Dec 27 2015 *)

PARI

my(x='x+O('x^40)); concat([0,0,0], Vec(x^4/((1+2*x)*(1-2*x+x^2+ 2*x^3)))) \\ G. C. Greubel, Aug 05 2019

Sage

a=(x^4/((1+2*x) * (1-2*x+x^2+2*x^3))).series(x, 40).coefficients(x, sparse=False); a[1:] # G. C. Greubel, Aug 05 2019

Formula

a(n)= 3*a(n-2) -4*a(n-3) -4*a(n-4).

a(n)= ((-2)^n -9*A077942(n) +20*A077942(n-1) -17*A077942(n-2))/32, n>3.

Extensions

Definition replaced with generating function. - the Assoc. Eds of the OEIS, Mar 28 2010