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.

0, -4, -6, -8, -7, -12, -13, -16, -14, -20, -20, -24, -21, -28, -27, -32, -28, -36, -34, -40, -35, -44, -41, -48, -42, -52, -48, -56, -49, -60, -55, -64, -56, -68, -62, -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

Offset: 0

Author

N. J. A. Sloane, Nov 08 2011

Keywords

• sign
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Bott, Raoul, Lectures on Morse theory, old and new, Bull. Amer. Math. Soc. 7 (1982), no. 2, 331-358; reprinted in Vol. 48 (October, 2011). See Eq. (4.30).
• Index entries for linear recurrences with constant coefficients, signature (0,1,0,1,0,-1).

Crossrefs

Cf. A047335, A008586 (signed bisections).

Programs

Magma

g:=0; m:=60; R:=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

Maple

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));
s:=g->seriestolist(series(f(g),x,60));
s(0);

Mathematica

LinearRecurrence[{0,1,0,1,0,-1},{0,-4,-6,-8,-7,-12},80] (* Harvey P. Dale, Jul 30 2019 *)

PARI

a(n)=if(n%2,,(n+5*I^n+3)/4)-2*n-2 \\ Charles R Greathouse IV, Nov 08 2011

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

Formula

a(n) = ((-1)^n+1)*(n+5*i^n+3)/8-2*(n+1). - Bruno Berselli, Nov 08 2011

G.f.: -x*(x+2)*(x^2+2*x+2) / ((x-1)^2*(x+1)^2*(x^2+1)). - Colin Barker, Jul 10 2015