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.

guess([1, 4, 11, 35, 98, 294, 832, 2401, 6774, 19137, 53466, 148994, 412233], [guessRat],
[guessSum, guessProduct], maxLevel==2)

(1)

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...

guessExpRat [(1+x)^x for x in 0..3]

(2)

A workaround is necessary, because of bug #128

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)]

(3)

guessPRec(q)(l, []).1

(4)

Here are some that are tried:

listA := [1,1,2,5,14,42,132];

listB := [1,2,6,21,80, 322];

listC := [1,1,2,7,42,429,7436,218348];

guess(listA, [guessRat], [guessSum, guessProduct])

(5)

guess(listB, [guessRat], [guessSum, guessProduct])

(6)

guess(listC, [guessRat], [guessProduct]).1

(7)

listD := [1,1,2,6,26,162,1450,18626];

listE := [1,1,2,6,28,202,2252];

guess(listD, [guessRat], [guessProduct]).1

   >> Error detected within library code:
   index out of range

li :=  [-86, -975, -100, -1728, -31213];

guess(li, [guessRat], [guessSum, guessProduct])

(8)

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

guessPRec([1,1,6,54,660,10260,194040,4326840,111177360,3234848400,105135861600]).1.function

(9)

guess([1,1,2,7,40,355,4720,91690,2559980,101724390], [guessRat], [guessSum, guessProduct],
maxLevel==2)

(10)

guess([1, 2, 3, 7, 11, 16, 26, 36, 56, 81, 131, 183, 287, 417, 677], [guessRat], [guessSum,
guessProduct], maxLevel==2)

(11)

guess([1,1,2,7,40,355,4720,91690,2559980,101724390,5724370860,455400049575], [guessRat],
[guessSum, guessProduct], maxLevel==2)

(12)

guess([1,1,4,35,545,13520,499215,26269200,1917388310,191268774585], [guessRat], [guessSum,
guessProduct], maxLevel==2)

(13)