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A123957
Expansion of g.f.: x^4/((1+2*x) * (1-2*x+x^2+2*x^3)).
1
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
1,6
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.
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 *)
PROG
(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
(Magma) R<x>:=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
(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
(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
CROSSREFS
Sequence in context: A208807 A126896 A334225 * A370625 A085285 A282250
KEYWORD
sign
AUTHOR
EXTENSIONS
Definition replaced with generating function. - the Assoc. Eds of the OEIS, Mar 28 2010
STATUS
approved