Neve,
to save you some time... see attachement.
BTW, look at the first 4 values in the result below.
Unfortunately, I do not see how one can extract from the result from
which point on it is valid. In fact, I find it a bit strange that it
doesn't agree at the beginning, but seemingly Martin Rubey and Waldek
Hebisch had their reasons or I do not understand why for f(0),...,f(3)
we just get 0*f(n)+0 = 0 from the guessing result.
Ralf
(1) -> l := [44, 178, 412, 746, 1168, 1669, 2260, 2941, 3712, 4573,
5524, 6565]
(1) [44, 178, 412, 746, 1168, 1669, 2260, 2941, 3712, 4573, 5524, 6565]
Type:
List(PositiveInteger)
(2) -> Z ==> Integer
Type:
Void
(3) -> E ==> Expression Z
Type:
Void
(4) -> K ==> Kernel E
Type:
Void
(5) -> P ==> Polynomial Z
Type:
Void
(6) -> e1 := guess(l).1
(6)
[
f(n):
4 3 2 6 5 4 3
(- n + 6 n - 11 n + 6 n)f(n) + 45 n - 174 n - 17 n + 402 n
+
2
128 n - 384 n
=
0
]
Type:
Expression(Integer)
(7) -> e2 := getEq(e1)$RecurrenceOperator(Z, E)
(7)
4 3 2 6 5 4 3
2
(- n + 6 n - 11 n + 6 n)f(n) + 45 n - 174 n - 17 n + 402 n +
128 n
+
- 384 n
Type:
Expression(Integer)
(8) -> k2 := mainKernel(e2)::K
(8) f(n)
Type:
Kernel(Expression(Integer))
(9) -> e3 := k2::E
(9) f(n)
Type:
Expression(Integer)
(10) -> e4 := eval(e2,e3,0)
6 5 4 3 2
(10) 45 n - 174 n - 17 n + 402 n + 128 n - 384 n
Type:
Expression(Integer)
(11) -> pol1 := e4::P
6 5 4 3 2
(11) 45 n - 174 n - 17 n + 402 n + 128 n - 384 n
Type:
Polynomial(Integer)
(12) -> e5 := (e2-e4)/e3
4 3 2
(12) - n + 6 n - 11 n + 6 n
Type:
Expression(Integer)
(13) -> pol2 := e5::P
4 3 2
(13) - n + 6 n - 11 n + 6 n
Type:
Polynomial(Integer)
(14) -> factor pol1
2
(14) (n - 3)(n - 2)(n - 1)n(45 n + 96 n + 64)
Type:
Factored(Polynomial(Integer))
(15) -> factor pol2
(15) - (n - 3)(n - 2)(n - 1)n
Type:
Factored(Polynomial(Integer))
(16) -> rat:=-pol1/pol2
2
(16) 45 n + 96 n + 64
Type:
Fraction(Polynomial(Integer))
(17) -> [eval(rat,n=i) for i in 0..12]
(17)
[64, 205, 436, 757, 1168, 1669, 2260, 2941, 3712, 4573, 5524, 6565, 7696]
Type:
List(Fraction(Polynomial(Integer)))
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--)clear complete
l := [44, 178, 412, 746, 1168, 1669, 2260, 2941, 3712, 4573, 5524, 6565]
Z ==> Integer
E ==> Expression Z
K ==> Kernel E
P ==> Polynomial Z
e1 := guess(l).1
e2 := getEq(e1)$RecurrenceOperator(Z, E)
k2 := mainKernel(e2)::K
e3 := k2::E
e4 := eval(e2,e3,0)
pol1 := e4::P
e5 := (e2-e4)/e3
pol2 := e5::P
factor pol1
factor pol2
rat:=-pol1/pol2
[eval(rat,n=i) for i in 0..12]
