A080369 a(n) is the value of Vandermonde determinant for lexicographically earliest n-mark Golomb-ruler.
1, 1, 6, 720, 6652800, 1693749657600, 367216146859161600000, 1888288177044984240734208000000, 4157567140515322460268246337585152000000000
Offset: 1
Keywords
Examples
n=6:the ruler={1,2,5,11,13,18}, the C[6,2]=15 possible differences={17,16,13,7,5,12,11,8,2,10,9,6,4,3,1}; the product = a(6)=1693749657600.
Programs
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Mathematica
t={marks of ruler}; lt=Length[t] b[x_] := Part[t, x] bd[x_] := Reverse[b[x]-Table[b[j], {j, 1, x-1}]] pb[x_] := Apply[Times, bd[x]] Table[{j, bd[j], pb[j]}, {j, 1, lt}]; vm=Table[Apply[Times, Table[pb[u], {u, 1, k}]], {k, 1, lt}]; Part[vm, lt]
Formula
a(n)=Product[a(i)-a(j)], j
A106668 Marks on lexicographically second 6-mark optimal Golomb ruler.
0, 1, 4, 10, 15, 17
Offset: 0
Links
- J. B. Shearer, Golomb Ruler Table
- Google Scholar
A106669 Marks on lexicographically third 6-mark optimal Golomb ruler.
0, 1, 8, 12, 14, 17
Offset: 0
Comments
Golomb ruler: Finite set with property that no difference between any two numbers is repeated and largest number is minimized.
Links
- J. B. Shearer, Golomb Ruler Table
- Google Scholar
A106670 Marks on fourth 6-mark optimal Golomb ruler.
0, 1, 8, 11, 13, 17
Offset: 0
Comments
Golomb ruler: Finite set with property that no difference between any two numbers is repeated and largest number is minimized.
Links
- J. B. Shearer, Golomb Ruler Table
- Google Scholar
Comments