OFFSET
0,3
COMMENTS
Inspired by sun flower spirals which come in Fib(i) and Fib(i+1) numbers in opposite directions. The present case of the Fib(n+1) X Fib(n) table has the following properties:
(i) Columns sum create the present irregular triangle.
(ii) Rows sum create the irregular triangle A268318.
(iii) The row sum of each of these irregular triangles is conjectured to be A000071.
(iv) The first differences of the sequence of half of the voids (0's) are conjectured to give A191797.
See illustrations in the links.
LINKS
Kival Ngaokrajang, Illustration of initial terms, Sun flower spirals
EXAMPLE
Irregular triangle begins:
1
2
2 2
2 3 2
2 3 2 3 2
2 3 2 3 3 2 3 2
2 3 2 3 3 2 3 2 3 3 2 3 2
...
PROG
(Small Basic)
TextWindow.Write("0, 1, 2, 2, 2, 2, 3, 2, ")
t[4][1] = 2
t[4][2] = 3
t[4][3] = 2
k[3] = 2
k[4] = 3
For n = 5 To 12
k[n] = k[n-1]+k[n-2]
c = math.Ceiling(k[n]/2)
i1 = 1
For j = 1 To k[n]
If Math.Remainder(k[n], 2)<>0 Then
If j > c then
t[n][j] = t[n][j-2*i1]
i1 = i1 + 1
Else
t[n][j] = t[n-1][j]
EndIf
Else
If j <= c then
t[n][j] = t[n-1][j]
Else
if j = c+1 Then
t[n][j] = t[n][j-1]
else
t[n][j] = t[n][j-(2*i1+1)]
i1 = i 1+ 1
endif
EndIf
EndIf
TextWindow.Write(t[n][j]+", ")
EndFor
EndFor
KEYWORD
nonn,base,tabf
AUTHOR
Kival Ngaokrajang, Feb 01 2016
STATUS
approved