OFFSET
0,6
COMMENTS
Refer to the construction rule used in A243618. For this case, the curvature is defined by (-1/k, 1/(k-1), 1), the circle radius will diverge to infinity (zero curvature). The integral curvatures appearing as periodic, i.e., 2, 6, 6, 10, 30, 42, 28, 12, ..., = A083482(k-1). The integral curvatures seem to align as some sequence, e.g., 3, 7, 13, 21, 31, 43, ..., = A002061(k) and 9, 25, 49, ..., = A016754(k-1). See illustration.
LINKS
Kival Ngaokrajang, Illustration for k = 2..7
EXAMPLE
Table begins:
n/k 2 3 4 5 6 7 ...
0 1 1 1 1 1 1 ...
1 1 1 1 1 1 1 ...
2 3 1 1 1 1 1 ...
3 5 2 1 1 1 1 ...
4 9 3 2 1 1 1 ...
5 13 5 3 2 1 1 ...
6 19 7 4 2 2 1 ...
7 25 9 5 3 2 2 ...
8 33 11 6 4 3 2 ...
9 41 14 7 5 3 2 ...
10 51 17 9 6 4 3 ...
11 61 21 11 7 5 3 ...
12 73 25 13 8 5 4 ...
...
PROG
(Small Basic)
For k=2 to 100
a=-k
b=k-1
c=1
aa[0][k]=1
For n = 1 To 100
x=a*b*c
y=Math.Power(x*(a+b+c), 1/2)
r=x/(a*b+a*c+b*c-2*y)
aa[n][k]= math.floor(1/r)
If 1/r-math.Floor(1/r)> 0.999999 Then
aa[n][k]=aa[n][k]+1
EndIf
c=r
EndFor
endFor
'=====================================
For t = 1 to 30
d=0
For nn=0 To t-1
kk=t+1-d
TextWindow.Write(aa[nn][kk]+", ")
d=d+1
EndFor
Endfor
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Kival Ngaokrajang, Jun 11 2014
STATUS
approved