OFFSET
0,4
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Paul Barry, Centered polygon numbers, heptagons and nonagons, and the Robbins numbers, arXiv:2104.01644 [math.CO], 2021.
Index entries for linear recurrences with constant coefficients, signature (1,-2,1).
FORMULA
a(0)=1, a(1)=1, a(2)=-1, a(n) = a(n-1) -2*a(n-2) +a(n-3) for n>=3. - Philippe Deléham, Sep 15 2006
a(n) = A000931(-2*n). - Michael Somos, Sep 18 2012
a(n) = A005314(-n-2). - Michael Somos, Dec 13 2013
a(n) = a(n-1) - 2*a(n-2) + a(n-3) for all n in Z. - Michael Somos, Dec 13 2013
EXAMPLE
G.f. = 1 + x - x^2 - 2*x^3 + x^4 + 4*x^5 - 7*x^7 - 3*x^8 + 11*x^9 + ...
MAPLE
seq(coeff(series(1/(1-x+2*x^2-x^3), x, n+1), x, n), n = 0..50); # G. C. Greubel, Aug 07 2019
MATHEMATICA
a[ n_] := If[ n < 0, SeriesCoefficient[ x^3 / (1 - 2 x + x^2 - x^3), {x, 0, -n}], SeriesCoefficient[ 1 / (1 - x + 2 x^2 - x^3), {x, 0, n}]]
LinearRecurrence[{1, -2, 1}, {1, 1, -1}, 50] (* G. C. Greubel, Aug 07 2019 *)
PROG
(PARI) {a(n) = if( n<0, polcoeff( x^3 / (1 - 2*x + x^2 - x^3) + x * O(x^-n), -n), polcoeff( 1 / (1 - x + 2*x^2 - x^3) + x * O(x^n), n))} /* Michael Somos, Sep 18 2012 */
(Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/(1-x+2*x^2-x^3) )); // G. C. Greubel, Aug 07 2019
(Sage) (1/(1-x+2*x^2-x^3)).series(x, 50).coefficients(x, sparse=False) # G. C. Greubel, Aug 07 2019
(GAP) a:=[1, 1, -1];; for n in [4..50] do a[n]:=a[n-1]-2*a[n-2]+a[n-3]; od; a; # G. C. Greubel, Aug 07 2019
CROSSREFS
KEYWORD
sign,easy
AUTHOR
N. J. A. Sloane, Nov 17 2002
STATUS
approved