|
|
A077889
|
|
Expansion of 1/( (1-x)*(1 + x^2 + x^3) ).
|
|
3
|
|
|
1, 1, 0, -1, 0, 2, 2, -1, -3, 0, 5, 4, -4, -8, 1, 13, 8, -13, -20, 6, 34, 15, -39, -48, 25, 88, 24, -112, -111, 89, 224, 23, -312, -246, 290, 559, -43, -848, -515, 892, 1364, -376, -2255, -987, 2632, 3243, -1644, -5874, -1598, 7519, 7473, -5920, -14991, -1552, 20912, 16544, -19359, -37455, 2816, 56815
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,6
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
a(n) = Sum_{k=0..floor(n/4)} A101950(n-3*k, k).
|
|
MAPLE
|
A101950 := proc(n, k) local j, k1: add((-1)^((n-j)/2)*binomial((n+j)/2, j)*(1+(-1)^(n+j))* binomial(j, k)/2, j=0..n) end: A077889 := proc(n): add(A101950(n-3*k, k), k=0..floor(n/4)) end: seq(A077889(n), n=0..60); # Johannes W. Meijer, Aug 06 2011
|
|
MATHEMATICA
|
CoefficientList[Series[1/((1-x)*(1+x^2+x^3)), {x, 0, 60}], x] (* or *) LinearRecurrence[{1, -1, 0, 1}, {1, 1, 0, -1}, 60] (* Harvey P. Dale, Jul 14 2017 *)
|
|
PROG
|
(PARI) my(x='x+O('x^60)); Vec(1/((1-x)*(1+x^2+x^3))) \\ G. C. Greubel, Dec 30 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( 1/((1-x)*(1+x^2+x^3)) )); // G. C. Greubel, Dec 30 2019
(Sage)
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 1/((1-x)*(1+x^2+x^3)) ).list()
(GAP) a:=[1, 1, 0, -1];; for n in [5..60] do a[n]:=a[n-1]-a[n-2]+a[n-4]; od; a; # G. C. Greubel, Dec 30 2019
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|