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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

Table of n, a(n) for n=0..45.

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 A276784 A153129

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 December 9 23:16 EST 2016. Contains 278993 sequences.