# Fibonacci

Thu Jun 3 07:01:36 CEST 2004

```    Hello, Seqfans.

These are generalizations of Fibonacci sequence.
I considered a sequence on a two dimensional cell space as follows.

a(7) a(8) a(9) a(10)
a(6) a(1) a(2) a(11)
a(5) a(4) a(3) a(12)
a(16)a(15)a(14)a(13)

It continues infinitely like a spiral.
.
Definition :
a(1)=1 , a(n)=a(n-1)+Sum{a(i) , a(i) contacts a(n-1)}
8 terms around a(m) contact  a(m).
So,
a(2)=a(1)                      =1
a(3)=a(1)+a(2)                 =2
a(4)=a(1)+a(2)+a(3)            =4
a(5)=a(1)+a(2)+a(3)+a(4)       =8
a(6)=a(1)+a(4)+a(5)            =13
a(7)=a(1)+a(4)+a(5)+a(6)       =26

a(n) : 1, 1, 2, 4, 8, 13, 26, 40, 81, 123, 205, 412, 620, 1034,

b(m) : 1, 1, 2, 3, 6, 9, 16, 25, 42, 68, 110, 179, 291, 470,
4 terms up-down-right-left of b(m) contact b(m).

c(m) : 0, 1, 1, 2, 4, 6, 12, 18, 37, 56, 94, 189,
The same definition as a(n) but a(1)=0, a(2)=1.

12 18 37 56
6  0  1  94
4  2  1  189

Tell me a good description of N line on OEIS for the sequences.

To Neil :
Are they fit to OEIS?

If you say Yes, then I will format them.

Yasutoshi

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