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last edited 8 months ago by beccari |
Edit detail for SandBox.GuessingSequence revision 17 of 598
added:
From Leonardo Sun Jul 20 07:23:09 -0700 2008
From: Leonardo
Date: Sun, 20 Jul 2008 07:23:09 -0700
Subject: fcorr
Message-ID: <20080720072309-0700@axiom-wiki.newsynthesis.org>
guess([-1/3,-11/25,-23/49,-13/27,-59/121,-83/169], [guessRat], [guessSum,
guessProduct], maxLevel==2)
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.
axiomguess([1, 4, 11, 35, 98, 294, 832, 2401, 6774, 19137, 53466, 148994, 412233], [guessRat], [guessSum, guessProduct], maxLevel==2)
 | (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 
being such a rational
function, there is no formula of the form 
or
, nor 
,
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...
axiomguessExpRat [(1+x)^x for x in 0..3]
 | (2) |
Type: List Record(function: Expression Integer,order: NonNegativeInteger?)
A workaround is necessary, because of bug #128
axioml := [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)]
 | (3) |
Type: List Polynomial Integer
axiomguessPRec(q)(l, []).1
 | (4) |
Type: Record(function: Expression Integer,order: NonNegativeInteger?)
Here are some that are tried:
axiomlistA := [1,1,2,5,14,42,132];
Type: List PositiveInteger?
axiomlistB := [1,2,6,21,80, 322];
Type: List PositiveInteger?
axiomlistC := [1,1,2,7,42,429,7436,218348];
Type: List PositiveInteger?
axiomguess(listA, [guessRat], [guessSum, guessProduct])
 | (5) |
Type: List Record(function: Expression Integer,order: NonNegativeInteger?)
axiomguess(listB, [guessRat], [guessSum, guessProduct])
 | (6) |
Type: List Record(function: Expression Integer,order: NonNegativeInteger?)
axiomguess(listC, [guessRat], [guessProduct]).1
 | (7) |
Type: Record(function: Expression Integer,order: NonNegativeInteger?)
axiomlistD := [1,1,2,6,26,162,1450,18626];
Type: List PositiveInteger?
axiomlistE := [1,1,2,6,28,202,2252];
Type: List PositiveInteger?
axiomguess(listD, [guessRat], [guessProduct]).1
>> Error detected within library code: index out of range
axiomli := [-86, -975, -100, -1728, -31213];
Type: List Integer
axiomguess(li, [guessRat], [guessSum, guessProduct])
 | (8) |
Type: List Record(function: Expression Integer,order: NonNegativeInteger?)
"Most" sequences arising in combinatorics are P-recursive:
axiomguessPRec([1,1,6,54,660,10260,194040,4326840,111177360,3234848400,105135861600]).1.function
 | (9) |
Type: Expression Integer
axiomguess([1,1,2,7,40,355,4720,91690,2559980,101724390], [guessRat], [guessSum, guessProduct], maxLevel==2)
 | (10) |
Type: List Record(function: Expression Integer,order: NonNegativeInteger?)
... --Thomas, Sun, 27 Jan 2008 04:29:36 -0800 reply
axiomguess([1, 2, 3, 7, 11, 16, 26, 36, 56, 81, 131, 183, 287, 417, 677], [guessRat], [guessSum, guessProduct], maxLevel==2)
 | (11) |
Type: List Record(function: Expression Integer,order: NonNegativeInteger?)
axiomguess([1,1,2,7,40,355,4720,91690,2559980,101724390,5724370860,455400049575], [guessRat], [guessSum, guessProduct], maxLevel==2)
 | (12) |
Type: List Record(function: Expression Integer,order: NonNegativeInteger?)
axiomguess([1,1,4,35,545,13520,499215,26269200,1917388310,191268774585], [guessRat], [guessSum, guessProduct], maxLevel==2)
 | (13) |
Type: List Record(function: Expression Integer,order: NonNegativeInteger?)
guess([-1/3,-11/25,-23/49,-13/27,-59/121,-83/169]?, [guessRat]?, [guessSum,
guessProduct], maxLevel==2)