cp's OEIS Frontend

A199626 G.f.: (1+x)^(2*g)*(1+x^3)^(3*g)/((1-x^2)*(1-x^4))-x^(2*g)*(1+x)^4/((1-x^2)*(1-x^4)) for g=0.

%I A199626 #28 Sep 08 2022 08:46:00
%S A199626 0,-4,-6,-8,-7,-12,-13,-16,-14,-20,-20,-24,-21,-28,-27,-32,-28,-36,
%T A199626 -34,-40,-35,-44,-41,-48,-42,-52,-48,-56,-49,-60,-55,-64,-56,-68,-62,
%U A199626 -72,-63,-76,-69,-80,-70,-84,-76,-88,-77,-92,-83,-96,-84,-100,-90,-104,-91,-108,-97,-112,-98,-116,-104,-120
%N A199626 G.f.: (1+x)^(2*g)*(1+x^3)^(3*g)/((1-x^2)*(1-x^4))-x^(2*g)*(1+x)^4/((1-x^2)*(1-x^4)) for g=0.
%H A199626 Colin Barker, <a href="/A199626/b199626.txt">Table of n, a(n) for n = 0..1000</a>
%H A199626 Bott, Raoul, <a href="http://dx.doi.org/10.1090/S0273-0979-1982-15038-8">Lectures on Morse theory, old and new</a>, Bull. Amer. Math. Soc. 7 (1982), no. 2, 331-358; reprinted in Vol. 48 (October, 2011). See Eq. (4.30).
%H A199626 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,1,0,-1).
%F A199626 a(n) = ((-1)^n+1)*(n+5*i^n+3)/8-2*(n+1). - _Bruno Berselli_, Nov 08 2011
%F A199626 G.f.: -x*(x+2)*(x^2+2*x+2) / ((x-1)^2*(x+1)^2*(x^2+1)). - _Colin Barker_, Jul 10 2015
%p A199626 f:=g->(1+x)^(2*g)*(1+x^3)^(3*g)/((1-x^2)*(1-x^4))-x^(2*g)*(1+x)^4/((1-x^2)*(1-x^4));
%p A199626 s:=g->seriestolist(series(f(g),x,60));
%p A199626 s(0);
%t A199626 LinearRecurrence[{0,1,0,1,0,-1},{0,-4,-6,-8,-7,-12},80] (* _Harvey P. Dale_, Jul 30 2019 *)
%o A199626 (Magma) g:=0; m:=60; R<x>:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!((1+x)^(2*g)*(1+x^3)^(3*g)/((1-x^2)*(1-x^4))-x^(2*g)*(1+x)^4/((1-x^2)*(1-x^4))));  // _Bruno Berselli_, Nov 08 2011
%o A199626 (PARI) a(n)=if(n%2,,(n+5*I^n+3)/4)-2*n-2 \\ _Charles R Greathouse IV_, Nov 08 2011
%o A199626 (PARI) concat(0, Vec(-x*(x+2)*(x^2+2*x+2)/((x-1)^2*(x+1)^2*(x^2+1)) + O(x^100))) \\ _Colin Barker_, Jul 10 2015
%Y A199626 Cf. A047335, A008586 (signed bisections).
%K A199626 sign,easy
%O A199626 0,2
%A A199626 _N. J. A. Sloane_, Nov 08 2011