(11C) Tribonacci Sequence

[Gamo]

The Tribonacci Sequence is a generalization of the Fibonacci sequence where each term is the sum of the three preceding terms.

The sequence begins 0, 1, 1, 2, 4, 7, 13, 24, 44, 81, 149,. . . .

Input the Nth number
Example: 7 A result 24
_______10 A result 149

Code:


LBL A
STO 0
19 
ENTER
33
√
3
x
- 
3
1/X
Y^X
STO 1
33
√
3
x
19
+
3
1/X
Y^X
STO 2
+
1
+
3
1/X
x
RCL 0
Y^X
STO 3
RCL 1
RCL 2
+
1
+
4
ENTER
3
/
x
RCL 1
RCL 2
+
1
+
X^2
9
1/X
x
-
1
-
STO 4
RCL 3
RCL 4
/
FIX 0
RTN

Gamo

[Dieter]

(12-14-2017 12:21 PM)Gamo Wrote:  The Tribonacci Sequence is a generalization of the Fibonacci sequence where each term is the sum of the three preceding terms.

The sequence begins 0, 1, 1, 2, 4, 7, 13, 24, 44, 81, 149,. . . .

Input the Nth number
Example: 7 A result 24
_______10 A result 149

Interesting formula. But implemented waaayyy too complicated. ;-)
Actually it's nothing more than u · vⁿ with u and v being two constants.

So what about this one:

Code:

LBL C
ENTER
1,839286755
STO 0
x<>y
y^x
RCL 0
4
x
RCL 0
x^2
-
1
-
/
,4
+
INT
RTN

Or simply...

Code:

LBL C
ENTER
1,839286755
x<>y
y^x
,336228117
x
,4
+
INT
RTN

Dieter

[StephenG1CMZ]

I am a little confused as to how a tribonacci sequence can be a generalisation of a Fibonacci - though to be fair Wikipedia also uses that terminology.
I'd have thought a tribonacci would be a variation, but an n-bonacci capable of handling any number of summations would be a generalisation.

But my main reason for posting isn't to quibble, but to enquire. I always find it helpful to think of applications to help focus upon the maths. Fibonacci always makes me think of rabbits, though I am sure that is not it's only use. Does the Tribonacci sequence have any practical use?

[Gamo]

Here is the detail on Phi and Tribonacci on YouTube.

https://youtu.be/e7SnRPubg-g

Gamo