Hexagonal Fibonacci

[y.kohmoto]

    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