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A074585
a(n)= Sum_{j=0..floor(n/2)} A073145(2*j + q), where q = 2*(n/2 - floor(n/2)).
1
3, -1, 2, 4, -3, 3, 8, -12, 11, 11, -30, 32, 13, -73, 96, -8, -157, 263, -110, -308, 685, -485, -504, 1676, -1653, -525, 3858, -4984, 605, 8239, -13824, 6192, 15875, -35889, 26210, 25556, -87651, 88307, 24904, -200860, 264267, -38501, -426622
OFFSET
0,1
COMMENTS
a(n) is the convolution of A073145(n) with the sequence (1,0,1,0,1,0, ...).
a(n) is also the sum of the reflected (see A074058) sequence of the generalized tribonacci sequence (A001644).
FORMULA
a(n) = -a(n-1) + 2*a(n-3) + a(n-4) - a(n-5), a(0) = 3, a(1) = -1, a(2) = 2, a(3) = 4, a(4) = -3.
G.f.: (3 + 2*x + x^2)/(1 + x - 2*x^3 - x^4 + x^5).
MATHEMATICA
CoefficientList[ Series[(3+2*x+x^2)/(1+x-2*x^3-x^4+x^5), {x, 0, 50}], x]
PROG
(PARI) my(x='x+O('x^50)); Vec((3+2*x+x^2)/(1+x-2*x^3-x^4+x^5)) \\ G. C. Greubel, Apr 13 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( (3+2*x+x^2)/(1+x-2*x^3-x^4+x^5) )); // G. C. Greubel, Apr 13 2019
(Sage) ((3+2*x+x^2)/(1+x-2*x^3-x^4+x^5)).series(x, 50).coefficients(x, sparse=False) # G. C. Greubel, Apr 13 2019
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Mario Catalani (mario.catalani(AT)unito.it), Aug 28 2002
EXTENSIONS
More terms from Robert G. Wilson v, Aug 29 2002
STATUS
approved