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 A124395 Expansion of (1-2x)/(1-2x+2x^3). 3
 1, 0, 0, -2, -4, -8, -12, -16, -16, -8, 16, 64, 144, 256, 384, 480, 448, 128, -704, -2304, -4864, -8320, -12032, -14336, -12032, 0, 28672, 81408, 162816, 268288, 373760, 421888, 307200, -133120, -1110016, -2834432, -5402624, -8585216, -11501568, -12197888 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Diagonal sums of number array A124394. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (2,0,-2). FORMULA a(n) = sum{k=0..floor(n/2), sum{j=0..k+1, C(k+1,j) C(n-j+1,2k+1) (-2)^j}}; a(n) = term (2,2) in the 3x3 matrix [2,1,0; 0,0,1; -2,0,0]^n. - Alois P. Heinz, Sep 10 2008 a(0)=1, a(1)=0, a(2)=0, a(n)=2*a(n-1)-2*a(n-3). - Harvey P. Dale, Dec 21 2013 a(n) = A077940(n)-2*A077940(n-1). - R. J. Mathar, Jan 25 2016 MAPLE a:= n-> (Matrix([[2, 1, 0], [0, 0, 1], [-2, 0, 0]])^n)[2, 2]: seq (a(n), n=0..35);  # Alois P. Heinz, Sep 10 2008 MATHEMATICA CoefficientList[Series[(1-2x)/(1-2x+2x^3), {x, 0, 50}], x] (* or *) LinearRecurrence[{2, 0, -2}, {1, 0, 0}, 50] (* Harvey P. Dale, Dec 21 2013 *) CROSSREFS Cf. A077940. Sequence in context: A050865 A288514 A282667 * A024908 A215459 A019442 Adjacent sequences:  A124392 A124393 A124394 * A124396 A124397 A124398 KEYWORD easy,sign AUTHOR Paul Barry, Oct 30 2006 STATUS approved

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Last modified February 16 08:26 EST 2019. Contains 320159 sequences. (Running on oeis4.)