OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,-2,-2).
FORMULA
a(n) = A077956(n) - A077956(n-1) = (-1)^(n-1)*(A077977(n) + A077977(n-1)). - G. C. Greubel, Jun 29 2019
EXAMPLE
G.f. = 1 - 2*x^2 - 4*X^3 + 12*X^5 + 20*X^6 - 4*X^7 - 68*X^8 - 100*X^9 + ... - Michael Somos, Jun 29 2019
MATHEMATICA
CoefficientList[Series[(1-x)/(1-x+2*x^2+2*x^3), {x, 0, 40}], x] (* or *) LinearRecurrence[{1, -2, -2}, {1, 0, -2}, 40] (* Harvey P. Dale, Mar 25 2018 *)
a[ n_] := LinearRecurrence[{1, -2, -2}, {1, 0, -2}, {n}][[1]]; (* Michael Somos, Jun 29 2019 *)
PROG
(PARI) my(x='x+O('x^40)); Vec((1-x)/(1-x+2*x^2+2*x^3)) \\ G. C. Greubel, Jun 29 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1-x)/(1-x+2*x^2+2*x^3) )); // G. C. Greubel, Jun 29 2019
(Sage) ((1-x)/(1-x+2*x^2+2*x^3)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Jun 29 2019
(GAP) a:=[1, 0, -2];; for n in [4..40] do a[n]:=a[n-1]-2*a[n-2]-2*a[n-3]; od; a; # G. C. Greubel, Jun 29 2019
CROSSREFS
KEYWORD
sign
AUTHOR
N. J. A. Sloane, Nov 17 2002
STATUS
approved