A090805 A simple recurrence with one error.

1, 2, 6, 21, 85, 430, 2586, 18109, 144880, 1303929, 13039300, 143432311, 1721187744, 22375440685, 313256169604, 4698842544075, 75181480705216, 1278085171988689, 23005533095796420, 437105128820131999, 8742102576402640000, 183584154104455440021, 4038851390298019680484

Offset

0,2

Comments

I included this in the OEIS only because was published on a web page. The explanation is my own - perhaps the original proposer had a different explanation.

References

Found on a puzzle page.

Links

Table of n, a(n) for n=0..22.

Hugo Delestinne, Meerdaelquiz

N. J. A. Sloane and Brady Haran, A Sequence with a Mistake, Numberphile video (2021)

Formula

a(0) = 1; a(n) = n*(a(n-1) + 1) but make an error if n = 4.

Hans Havermann points out that the first 7 terms could also be produced by the recurrence f[x] = f[x - 1]*(x - 1) + GCD[3*f[x - 1], (x - 1)] with f[1] = 1. (This gives the continuation 1, 2, 6, 21, 85, 430, 2586, 18103, 144825, 1303434, 13034342, ...) But given the nature of the other problems on this quiz, I think my explanation is more likely.

Example

1..add.1..multiply.by 1 -> 2
2..add.1..multiply.by 2 -> 6
6......1............. 3 -> 21
21.....1............. 4 -> 88 but here you make a mistake and instead multiply by 4 and add 1, getting 85
85.....1............. 5 -> 430
430....1............. 6 -> 2586
etc

Maple

a:= proc(n) a(n):= n*a(n-1) + `if`(n=4, 1, n) end: a(0):= 1:
seq(a(n), n=0..22);  # Alois P. Heinz, May 14 2021

Mathematica

a={1}; Do[n=Length[a]; a=Append[a, If[n==4, Last[a]n+1, (Last[a]+1)n]], 22]; a (* Jake L Lande, Jul 28 2024 *)

Crossrefs

Cf. A033540, A344229.

Sequence in context: A099947 A121726 A344229 * A150226 A326335 A256180

Adjacent sequences: A090802 A090803 A090804 * A090806 A090807 A090808

Keyword

nonn,easy,dumb

Author

N. J. A. Sloane, Feb 12 2004

Status

approved