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This page makes test uses of the guessing package by Martin Rubey. Feel free to add new sequences or change the sequences to ones you like to try.

See GuessingFormulasForSequences for some explanations.

axiom
guess([1, 4, 11, 35, 98, 294, 832, 2401, 6774, 19137, 53466, 148994, 412233], [guessRat],
[guessSum, guessProduct], maxLevel==2)
LatexWiki Image(1)
Type: List Record(function: Expression Integer,order: NonNegativeInteger)

The answer being an empty list tells us, that there is no rational function of total degree less than 13, that generates these numbers. Furthermore, for LatexWiki Image being such a rational function, there is no formula of the form LatexWiki Image or LatexWiki Image, nor LatexWiki Image, nor replacing the products by sums. In fact, if you look at Sloane's encyclopedia, you will find a good reason for that: I'd by very surprised to find such a simple formula for such a family of objects...

axiom
guessExpRat [(1+x)^x for x in 0..3]
LatexWiki Image(2)
Type: List Record(function: Expression Integer,order: NonNegativeInteger)

A workaround is necessary, because of bug #128

axiom
l := [1, 1, 1+q, 1+q+q^2, 1+q+q^2+q^3+q^4, 1+q+q^2+q^3+2*q^4+q^5+q^6,
1+q+q^2+q^3+2*q^4+2*q^5+2*q^6+q^7+q^8+q^9,
(1+q^4+q^6)*(1+q+q^2+q^3+q^4+q^5+q^6),
(1+q^4)*(1+q+q^2+q^3+q^4+q^5+2*q^6+2*q^7+2*q^8+2*q^9+q^10+q^11+q^12)]
LatexWiki Image(3)
Type: List Polynomial Integer
axiom
guessPRec(q)(l, []).1
LatexWiki Image(4)
Type: Record(function: Expression Integer,order: NonNegativeInteger)

Here are some that are tried:

axiom
listA := [1,1,2,5,14,42,132];
Type: List PositiveInteger
axiom
listB := [1,2,6,21,80, 322];
Type: List PositiveInteger
axiom
listC := [1,1,2,7,42,429,7436,218348];
Type: List PositiveInteger
axiom
guess(listA, [guessRat], [guessSum, guessProduct])
LatexWiki Image(5)
Type: List Record(function: Expression Integer,order: NonNegativeInteger)
axiom
guess(listB, [guessRat], [guessSum, guessProduct])
LatexWiki Image(6)
Type: List Record(function: Expression Integer,order: NonNegativeInteger)
axiom
guess(listC, [guessRat], [guessProduct]).1
LatexWiki Image(7)
Type: Record(function: Expression Integer,order: NonNegativeInteger)

axiom
listD := [1,1,2,6,26,162,1450,18626];
Type: List PositiveInteger
axiom
listE := [1,1,2,6,28,202,2252];
Type: List PositiveInteger
axiom
guess(listD, [guessRat], [guessProduct]).1
>> Error detected within library code: index out of range

axiom
li :=  [-86, -975, -100, -1728, -31213];
Type: List Integer
axiom
guess(li, [guessRat], [guessSum, guessProduct])
LatexWiki Image(8)
Type: List Record(function: Expression Integer,order: NonNegativeInteger)

"Most" sequences arising in combinatorics are P-recursive:

axiom
guessPRec([1,1,6,54,660,10260,194040,4326840,111177360,3234848400,105135861600]).1.function
LatexWiki Image(9)
Type: Expression Integer

axiom
guess([1,1,2,7,40,355,4720,91690,2559980,101724390], [guessRat], [guessSum, guessProduct],
maxLevel==2)
LatexWiki Image(10)
Type: List Record(function: Expression Integer,order: NonNegativeInteger)

axiom
guess([1, 2, 3, 7, 11, 16, 26, 36, 56, 81, 131, 183, 287, 417, 677], [guessRat], [guessSum,
guessProduct], maxLevel==2)
LatexWiki Image(11)
Type: List Record(function: Expression Integer,order: NonNegativeInteger)

axiom
guess([1,1,2,7,40,355,4720,91690,2559980,101724390,5724370860,455400049575], [guessRat],
[guessSum, guessProduct], maxLevel==2)
LatexWiki Image(12)
Type: List Record(function: Expression Integer,order: NonNegativeInteger)

axiom
guess([1,1,4,35,545,13520,499215,26269200,1917388310,191268774585], [guessRat], [guessSum,
guessProduct], maxLevel==2)
LatexWiki Image(13)
Type: List Record(function: Expression Integer,order: NonNegativeInteger)




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