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A165795 Table T(n,m) = numerator of 1/n^2-1/m^2 read by antidiagonals, T(0,k)=1 and T(n,0)=-1. 4
1, -1, 1, -1, 0, 1, -1, -3, 3, 1, -1, -8, 0, 8, 1, -1, -15, -5, 5, 15, 1, -1, -24, -3, 0, 3, 24, 1, -1, -35, -21, -7, 7, 21, 35, 1, -1, -48, -2, -16, 0, 16, 2, 48, 1, -1, -63, -45, -1, -9, 9, 1, 45, 63, 1, -1, -80, -15, -40, -5, 0, 5, 40, 15, 80, 1, -1, -99, -77, -55, -33, -11, 11 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

A row of T(0,k)= 1 is added on top of the array shown in A172157, which is then read upwards by antidiagonals.

One may also interpret this as appending a 1 to each row of A173651 or adding a column of -1's and a diagonal of +1's to A165507.

LINKS

Table of n, a(n) for n=0..72.

FORMULA

T(n,0) = -A158388(n).

T(n,k) = A172157(n,k), n>=1.

EXAMPLE

The array of numerators starts in row n=0 with columns m>=0 as:

.1...1...1...1...1...1...1...1...1...1...1.

-1...0...3...8..15..24..35..48..63..80..99. A005563, A147998

-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

CROSSREFS

Cf. A165507, A173651.

Sequence in context: A196904 A197373 A197529 * A287290 A287981 A213660

Adjacent sequences:  A165792 A165793 A165794 * A165796 A165797 A165798

KEYWORD

frac,tabl,easy,sign

AUTHOR

Paul Curtz, Sep 27 2009

STATUS

approved

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Last modified October 24 17:11 EDT 2021. Contains 348233 sequences. (Running on oeis4.)