A172157 Triangle T(n,m) = numerator of 1/n^2 - 1/m^2, read by rows, with T(n,0) = -1.

-1, -1, -3, -1, -8, -5, -1, -15, -3, -7, -1, -24, -21, -16, -9, -1, -35, -2, -1, -5, -11, -1, -48, -45, -40, -33, -24, -13, -1, -63, -15, -55, -3, -39, -7, -15, -1, -80, -77, -8, -65, -56, -5, -32, -17, -1, -99, -6, -91, -21, -3, -4, -51, -9, -19, -1, -120, -117, -112

Offset

1,3

Comments

The triangle obtained by negating the values of the triangle A120072 and adding a row T(n,0) = -1.

Links

G. C. Greubel, Rows n=1..100 of triangle, flattened

Example

The full array of numerators starts in row n=1 with columns m>=0 as:
-1...0...3...8..15..24..35..48..63..80..99. A005563
-1..-3...0...5...3..21...2..45..15..77...6. A061037, A070262
-1..-8..-5...0...7..16...1..40..55...8..91. A061039
-1.-15..-3..-7...0...9...5..33...3..65..21. A061041
-1.-24.-21.-16..-9...0..11..24..39..56...3. A061043
-1.-35..-2..-1..-5.-11...0..13...7...5...4. A061045
-1.-48.-45.-40.-33.-24.-13...0..15..32..51. A061047
-1.-63.-15.-55..-3.-39..-7.-15...0..17...9. A061049
The triangle is the portion below the main diagonal, left from the zeros, 0<=m<n.

Mathematica

T[n_, 0] := -1; T[n_, k_] := 1/n^2 - 1/k^2; Table[Numerator[T[n, k]], {n, 1, 100}, {k, 0, n - 1}] // Flatten (* G. C. Greubel, Sep 19 2018 *)

Crossrefs

Cf. A172370, A174233, A165795.

Sequence in context: A021318 A068437 A016477 * A209136 A206800 A258205

Adjacent sequences: A172154 A172155 A172156 * A172158 A172159 A172160

Keyword

sign,frac,easy,tabl

Author

Paul Curtz, Jan 27 2010

Status

approved