cp's OEIS Frontend

A138019 Period 5: repeat [1, 1, 0, -1, -1].

%I A138019 #23 Dec 12 2023 08:42:38
%S A138019 1,1,0,-1,-1,1,1,0,-1,-1,1,1,0,-1,-1,1,1,0,-1,-1,1,1,0,-1,-1,1,1,0,-1,
%T A138019 -1,1,1,0,-1,-1,1,1,0,-1,-1,1,1,0,-1,-1,1,1,0,-1,-1,1,1,0,-1,-1,1,1,0,
%U A138019 -1,-1,1,1,0,-1,-1,1,1,0,-1,-1,1,1,0,-1,-1,1,1,0,-1,-1,1,1,0,-1,-1,1,1,0,-1,-1,1,1,0,-1,-1,1,1,0,-1
%N A138019 Period 5: repeat [1, 1, 0, -1, -1].
%H A138019 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (-1, -1, -1, -1).
%F A138019 Inverse binomial transform of A138003.
%F A138019 O.g.f.: (1+x)(x^2+x+1)/(1+x+x^2+x^3+x^4). - _R. J. Mathar_, Jun 28 2008
%F A138019 Euler transform of length 5 sequence [ 1, -1, -1, 0, 1]. - _Michael Somos_, Jun 17 2015
%F A138019 G.f.: (1 - x^2 ) * (1 - x^3) / ((1 - x) * (1 - x^5)). - _Michael Somos_, Jun 17 2015
%F A138019 a(n) = -a(-1-n) = a(n+5) for all n in Z. - _Michael Somos_, Jun 17 2015
%e A138019 G.f. = 1 + x - x^3 - x^4 + x^5 + x^6 - x^8 - x^9 + x^10 + x^11 - x^13 + ...
%p A138019 A138019 := proc(n)
%p A138019     op( 1+modp(n,5),[1,1,0,-1,-1]) ;
%p A138019 end proc:
%p A138019 seq(A138019(n),n=0..30) ; # _R. J. Mathar_, Feb 12 2021
%t A138019 a[ n_] := Sign[2 - Mod[n, 5]]; (* _Michael Somos_, Jun 17 2015 *)
%t A138019 PadRight[{},120,{1,1,0,-1,-1}] (* _Harvey P. Dale_, Oct 06 2023 *)
%o A138019 (PARI) a(n)=sign(2-n%5) /* _Jaume Oliver Lafont_, Aug 28 2009 */
%Y A138019 Cf. A080891, A105368.
%K A138019 easy,sign
%O A138019 0,1
%A A138019 _Paul Curtz_, May 01 2008