Fibonacci
y.kohmoto
zbi74583 at boat.zero.ad.jp
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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