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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 (list; graph; refs; listen; history; text; internal format)
 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). LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (-1,0,2,1,-1). 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:=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 Cf. A073145, A074058, A001644, A074331, A074392, A074475. Sequence in context: A209301 A049992 A227147 * A183312 A108038 A151845 Adjacent sequences:  A074582 A074583 A074584 * A074586 A074587 A074588 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

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Last modified March 29 21:32 EDT 2020. Contains 333117 sequences. (Running on oeis4.)