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

1,3

Links

Table of n, a(n) for n=1..9.

Formula

a(n)=Product[a(i)-a(j)], j<i<=n; product of C[n, 2] positive differences provided by the n marks of ruler.

Example

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.

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]

Crossrefs

Cf. A031869-A031875.

Sequence in context: A052295 A169668 A168467 * A036981 A343434 A202080

Adjacent sequences: A080366 A080367 A080368 * A080370 A080371 A080372

Keyword

nonn

Author

Labos Elemer, Feb 24 2003

Status

approved