Table for the Half Fibonacci Series and the Algorithm 4 to 5 Series.

n	Fib n and Fib n 1/2	Alg 4 to 5
0	0
	½
1	1
2	1
2 ½	1 ½
3	2
3 ½	2 ½
4	3	4
4 ½	4	5
5	5	7
5 ½	6 ½	6
6	8	8
6 ½	10 ½	10
7	13	12
7 ½	17	15
8	21	18
8 ½	27 ½	22, 27
9	34	33
9 ½	44 ½	41
10	55	51
10 ½	72	63
11	89	78
11 ½	116 ½	97
12	144	121
12 ½	188 ½	151, 188
13	233	235
13 ½	305	293
14	377	366
14 ½	493 ½	457
15	610	571
15 ½	798 ½	713
16	987	891
16 ½	1292	1113
17	1597	1391
17 ½	2090 ½	1738, 2172
18	2584	2715
18 ½	3382 ½	3430
19	4181	4287
19 ½	5473	5358
20	6765	6697
20 ½	8855 ½	8371
21	10946	10463
		13078
22	17711	16347

Note:

Fib n ½ = 1/2 Fib( n + 2)

Eg F 19 ½ = ½ F 21

5473 = ½ 10946

F16½ = 1292 = ½ F18

= ½ x 2584

F18 ½ = 3382 ½

= ½ x F20 = ½ x 6765

F8½ = ½ F10

=27½ = ½ x 55

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Fn½ - Fn = F(n-2½)

F18½ - F18 = F15½?

3382.5 – 2584 = 798.5

 = yes

F15½ -F15 = F12½

798½ - 610 = 188½

=yes

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OK  This is how it looks when it is typed with table grid on Word Document, then copied (control c) and pasted (control v)  onto blog post.

Maybe this is better than my handwritten Tables....

There are interesting new equations and equivalences here...some are as just above.

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One can see that the 4 to 5 series follows the half Fibonacci series to some small degree,  but numbers begin to diverge widely as the Series ascends.

I have previously worked out how to micro adjust  numbers at the end of the crochet  or knit work to exactly follow the Fib and a half Series
 see 9/13/14 ie 13th Sept 2014 for 3 tables describing
progress visually, like a map.
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Next I can give you a map of how the 4 to 5 Series grows...   as soon as the diagrams are drawn........

1/8/2017    ***Column 3 on this post. shows how the 4 to 5 series grows
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