A182848 Joint-rank array of the numbers j*(i-1+r), where r=sqrt(5), i>=1, j>=1, by antidiagonals.

1, 4, 2, 8, 7, 3, 12, 14, 11, 5, 17, 22, 21, 16, 6, 24, 30, 33, 29, 20, 9, 28, 40, 45, 44, 38, 26, 10, 35, 51, 59, 61, 57, 47, 32, 13, 41, 60, 73, 80, 77, 69, 56, 37, 15, 49, 71, 88, 97, 101, 94, 84, 66, 43, 18, 55, 82, 103, 115, 124, 123, 113, 99, 76, 50, 19, 64

Offset

1,2

Comments

Joint-rank arrays are defined in the first comment at A182801.

Links

Table of n, a(n) for n=1..67.

Formula

T(i,j) = Sum_{floor(j*(i-1+r)/(k-1+r): r=sqrt(5), k>=1} for i>=1, j>=1.

Example

Northwest corner:
1....4....8...12...17...
2....7...14...22...30...
3...11...21...33...45...
5...16...29...44...61...

Mathematica

r=Sqrt[5];
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

Cf. A182801, A182846.

Sequence in context: A098798 A131783 A094312 * A228834 A197016 A198145

Adjacent sequences: A182845 A182846 A182847 * A182849 A182850 A182851

Keyword

nonn,tabl

Author

Clark Kimberling, Dec 08 2010

Status

approved