[seqfan] sequence defined by ``exotic addition''

[Georgi Guninski]

define binary operation "o" on pairs a,b:
a o b = a[1]+b[1] , a[1]*b[2]+a[2]*b[1]

define scalar multiplication "x":
2n x a = (n x a) o (n x a)
2n+1 x a= ((n x a) o (n x a)) o a
1 x a = a


the sequence a(n) is the second component of n x [1,1]:
1,2,4,8,12,24,40,64,72,144,224,320,416,576,768,1024,1040 ...

the sequence may be more interesting if "o" were associative, is there a
list of binary associative functions?

attached is a sample pari implementation.

superseeker claims to find degree 15 revogf.

thanks.

-- 
georgi
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{
radd(a,b)=
return([a[1]+b[1],a[1]*b[2]+a[2]*b[1]]);
}

{
rellpow(a,b)=
local(xx,yy,z,d);
xx=a;yy=b;z=a;
if(b==1,return(a));
yy=yy-1;
while(yy!=0,
while( yy % 2 == 0, yy=yy/2;xx=radd(xx,xx););
yy=yy-1;
z=radd(z,xx); 
);
return(z);
}
{
aa(n)=return(rellpow([1,1],n)[2])
}