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A182847
Joint-rank array of the numbers j*(i-1+r), where r=sqrt(3), i>=1, j>=1, by diagonals.
3
1, 3, 2, 6, 7, 4, 10, 13, 11, 5, 14, 20, 21, 16, 8, 18, 27, 32, 30, 22, 9, 24, 36, 42, 44, 38, 26, 12, 29, 46, 55, 61, 58, 49, 33, 15, 34, 54, 69, 77, 78, 72, 59, 40, 17, 39, 64, 84, 95, 100, 98, 87, 70, 47, 19, 45, 73, 97, 113, 123, 124, 117, 103, 80
OFFSET
1,2
COMMENTS
Joint-rank arrays are defined in the first comment at A182801.
FORMULA
T(i,j)=sum(k>=1, floor( j*(i-1+r)/(k-1+r) ) ) where r=sqrt(3), for i>=1, j>=1.
EXAMPLE
Northwest corner:
1....3....6...10...
2....7...13...20...
4...11...21...32...
5...16...30...44...
MATHEMATICA
r=Sqrt[3];
f[i_, j_]:=Sum[Floor[j*(i-1+r)/(k-1+r)], {k, 1, 1+r+j(i-1+r)}];
TableForm[Table[f[i, j], {i, 1, 10}, {j, 1, 10}]]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Dec 08 2010
STATUS
approved