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 A078001 Expansion of (1-x)/(1-2*x+x^2+x^3). 2
 1, 1, 1, 0, -2, -5, -8, -9, -5, 7, 28, 54, 73, 64, 1, -135, -335, -536, -602, -333, 472, 1879, 3619, 4887, 4276, 46, -9071, -22464, -35903, -40271, -22175, 31824, 126094, 242539, 327160, 285687, 1675, -609497, -1506356, -2404890, -2693927, -1476608, 2145601, 8461737, 16254481, 21901624 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Index entries for linear recurrences with constant coefficients, signature (2, -1, -1). FORMULA a(n) = Sum_{k=0..floor(n/3)} (-1)^k*binomial(n-k, 2*k). - Vladeta Jovovic, Feb 10 2003 a(0)=1, a(n+1)=a(n) - Sum_{k=0..n-2} a(k). - Alex Ratushnyak, May 03 2012 a(0)=1, a(1)=1, a(2)=1, a(n)=2*a(n-1)-a(n-2)-a(n-3). - Harvey P. Dale, Nov 03 2013 MATHEMATICA CoefficientList[Series[(1-x)/(1-2x+x^2+x^3), {x, 0, 50}], x] (* or *) LinearRecurrence[{2, -1, -1}, {1, 1, 1}, 50] (* Harvey P. Dale, Nov 03 2013 *) PROG (Python) a = [1]*1000 for n in range(55): .    print a[n], .    sum=0 .    for k in range(n-1): .    .    sum+=a[k] .    a[n+1] = a[n]-sum # from Alex Ratushnyak, May 03 2012 (PARI) Vec((1-x)/(1-2*x+x^2+x^3)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012 CROSSREFS Cf. A005251, A077856. Sequence in context: A011279 A185094 A071099 * A072955 A288730 A276784 Adjacent sequences:  A077998 A077999 A078000 * A078002 A078003 A078004 KEYWORD sign,easy AUTHOR N. J. A. Sloane, Nov 17 2002 STATUS approved

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Last modified April 18 22:08 EDT 2019. Contains 322237 sequences. (Running on oeis4.)