Closed ckrause closed 8 months ago
Example:
; A275698: a(0) = 2, after that a(n) is 3 plus the least common multiple of previous terms. ; Formula: a(n) = a(n-1)*b(n-1)+3, a(1) = 5, a(0) = 2, b(n) = a(n-1)*b(n-1), b(1) = 2, b(0) = 1 mov $1,1 mov $2,2 lpb $0 sub $0,1 mul $1,$2 mov $2,$1 add $2,3 lpe mov $0,$2
Notice that:
a(n) = a(n-1)*b(n-1)+3 b(n) = a(n-1)*b(n-1)
subtract the two equations we obtain
a(n)-b(n) = 3
and thus b(n) = a(n)-3. Therefore we can simplify the main formula to a(n) = a(n-1)*(a(n-1)-3)+3.
b(n) = a(n)-3
a(n) = a(n-1)*(a(n-1)-3)+3
Similar approach should work for:
; A081367: E.g.f.: exp(2*x)/sqrt(1-2*x). ; Formula: a(n) = b(n-1)*(2*n-2)+2*a(n-1)+a(n-1), a(2) = 11, a(1) = 3, a(0) = 1, b(n) = b(n-1)*(2*n-2)+a(n-1), b(2) = 5, b(1) = 1, b(0) = 0 mov $2,1 lpb $0 sub $0,1 mul $3,$1 add $3,$2 add $1,2 mul $2,2 add $2,$3 lpe mov $0,$2
Example:
Notice that:
subtract the two equations we obtain
and thus
b(n) = a(n)-3
. Therefore we can simplify the main formula toa(n) = a(n-1)*(a(n-1)-3)+3
.Similar approach should work for: