OFFSET
0,3
LINKS
Robert Israel, Table of n, a(n) for n = 0..1739
FORMULA
G.f: (1-z + sqrt(1-6*z+13*z^2+4*z^3-4*z^4))/(2*(z-z^2)).
D-finite with recurrence: +(n+1)*a(n) +(-7*n+2)*a(n-1) +(19*n-29)*a(n-2) +3*(-3*n+4)*a(n-3) +2*(-4*n+17)*a(n-4) +4*(n-5)*a(n-5)=0. - R. J. Mathar, Mar 02 2016
Recurrence follows from the differential equation -1+5*z+3*z^2-5*z^3+2*z^4 + (1-5*z+9*z^2-15*z^3+2*z^4)*g(z) + (z-7*z^2+19*z^3-9*z^4-8*z^5+4*z^6)*g'(z) satisfied by the g.f. - Robert Israel, Jul 14 2017
EXAMPLE
a(2)=2*1*0-4=-4. a(3)=2*1*(-4)-4+0^2-2=-14. a(4)=2*1*(-14)-4+2*0*(-4)-4=-36.
MAPLE
l:=0: : k := -2 : m:=0:d(0):=1:d(1):=m: for n from 1 to 30 do d(n+1):=sum(d(p)*d(n-p)+k, p=0..n)+l:od :
taylor((1-sqrt(1-4*z*(d(0)-z*d(0)^2+z*m+(k+l)*z^2/(1-z)+k*z^2/(1-z)^2)))/(2*z), z=0, 30); seq(d(n), n=0..30);
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Richard Choulet, May 03 2010
EXTENSIONS
G.f. edited, and more terms, from Robert Israel, Jul 14 2017
STATUS
approved