# Hexagonal Fibonacci

y.kohmoto zbi74583 at boat.zero.ad.jp
Fri Jun 18 07:16:54 CEST 2004

```    Hello, seqfans.
I considerd the same kind of generalized Fibonacci as A094767

http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?An
um=A094767

To Neil :
If they are good, add them on OEIS.

Yasutoshi

%I  A000001
%S A000001 1, 1, 2, 4, 7, 12, 20, 34, 55, 90, 148, 240, 394, 638
%N A000001 A hexagonal spiral Fibonacci sequence
%C A000001 Consider  the following spiral :
%C A000001                       a(6)  a(7)  a(8)
%C A000001                    a(5)  a(1)  a(2)  a(9)
%C A000001                 a(14) a(4)  a(3)  a(10)
%C A000001                    a(13) a(12) a(11)
%C A000001   Then
%C A000001   a(1)=1 , a(n)=a(n-1)+Sum{a(i) : a(i) adjacent to a(n-1)}
%C A000001   Here 6 terms around a(m) touch  a(m).
%C A000001   then a(n) satisfies
%C A000001   a(2)=a(1)                      =1
%C A000001   a(3)=a(1)+a(2)                 =2
%C A000001   a(4)=a(1)+a(2)+a(3)            =4
%C A000001   a(5)=a(1)+a(3)+a(4)            =7
%C A000001   a(6)=a(1)+a(4)+a(5)            =12
%C A000001   a(7)=a(1)+a(5)+a(6)            =20
%C A000001   table :
%C A000001                     12    20   34
%C A000001                  7     1     1     55
%C A000001               638   4     2     90
%C A000001                 394    240  148
%K A000001 nonn
%O A000001 1, 3
%A A000001 Yasutoshi Kohmoto (zbi74583 at boat.zero.ad.jp)
%Y A000001 A000002

%I  A000002
%S  A000002 0, 1, 1, 2, 3, 5, 8, 14, 23, 38, 63, 102,168, 272
%N  A000002  A hexagonal spiral Fibonacci sequence
%C  A000002  Consider  the following spiral :
%C  A000002                       a(6)  a(7)  a(8)
%C  A000002                    a(5)  a(1)  a(2)  a(9)
%C  A000002                 a(14) a(4)  a(3)  a(10)
%C  A000002                    a(13) a(12) a(11)
%C  A000002   Then
%C  A000002   a(1)=0 , a(2)=1, a(n)=a(n-1)+Sum{a(i) , a(i) is adjacent to
a(n-1)}
%C  A000002   6 terms around a(m) touch  a(m).
%C  A000002   table :
%C  A000002                    5    8    14
%C  A000002                  3    0    1    23
%C  A000002               272   2    1   38
%C A000002                   168  102  63
%K A000002  nonn
%O A000002  0, 4
%A A000002 Yasutoshi Kohmoto (zbi74583 at boat.zero.ad.jp)
%Y A000002 A000001

```