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A077913 Expansion of 1/((1-x)*(1+x+2*x^2+x^3)). 1
1, 0, -1, 1, 2, -2, -2, 5, 2, -9, 1, 16, -8, -24, 25, 32, -57, -31, 114, 6, -202, 77, 322, -273, -447, 672, 496, -1392, -271, 2560, -625, -4223, 2914, 6158, -7762, -7467, 16834, 5863, -32063, 3504, 54760, -29704, -83319, 87968, 108375, -200991, -103726, 397334, 11110, -702051, 282498, 1110495 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,5
LINKS
FORMULA
G.f.: 1-x^2/(U(0)+x^2) where U(k)= 1 + (1+x)*x/( 1 - (1+x)*x/((1+x)*x + 1/U(k+1))) ; (continued fraction, 2-step). - Sergei N. Gladkovskii, Oct 24 2012
5*a(n) = 1 + 4*A077979(n) + 3*A077979(n-1) + A077979(n-2). - R. J. Mathar, Jul 10 2013
MATHEMATICA
LinearRecurrence[{0, -1, 1, 1}, {1, 0, -1, 1}, 60] (* or *) CoefficientList[ Series[1/((1-x)*(1+x+2*x^2+x^3)), {x, 0, 60}], x] (* G. C. Greubel, Jul 02 2019 *)
PROG
(PARI) my(x='x+O('x^60)); Vec(1/((1-x)*(1+x+2*x^2+x^3))) \\ G. C. Greubel, Jul 02 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( 1/((1-x)*(1+x+2*x^2+x^3)) )); // G. C. Greubel, Jul 02 2019
(Sage) (1/((1-x)*(1+x+2*x^2+x^3))).series(x, 60).coefficients(x, sparse=False) # G. C. Greubel, Jul 02 2019
(GAP) a:=[1, 0, -1, 1];; for n in [5..60] do a[n]:=-a[n-2]+a[n-3]+a[n-4]; od; a; # G. C. Greubel, Jul 02 2019
CROSSREFS
Sequence in context: A363924 A096396 A029662 * A069862 A075002 A228917
KEYWORD
sign,easy
AUTHOR
N. J. A. Sloane, Nov 17 2002
STATUS
approved

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Last modified March 5 08:03 EST 2024. Contains 370538 sequences. (Running on oeis4.)