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A280579 Square array read by antidiagonals downwards giving the first differences A261327(n+p) - A261327(n), with p >= 0. 1

%I

%S 0,0,4,0,-3,1,0,11,8,12,0,-8,3,0,4,0,24,16,27,24,28,0,-19,5,-3,8,5,9,

%T 0,43,24,48,40,51,48,52,0,-36,7,-12,12,4,15,12,16,0,68,32,75,56,80,72,

%U 83,80,84,0,-59,9,-27

%N Square array read by antidiagonals downwards giving the first differences A261327(n+p) - A261327(n), with p >= 0.

%C Successive rows:

%C p

%C 0: 0, 0, 0, 0, 0, 0, 0, ...

%C 1: 4, -3, 11, -8, 24, -19, 43, ...

%C 2: 1, 8, 3, 16, 5, 24, 7, ...

%C 3: 12, 0, 27, -3, 48, -12, 75, ...

%C 4: 4, 24, 8, 40, 12, 56, 16, ...

%C 5: 28, 5, 51, 4, 80, -3, 115, ...

%C 6: 9, 48, 15, 72, 21, 96, 27, ...

%C ... .

%C Main diagonal: alternate 3*n^2, -3.

%C From p>0, the rows are multiples of 1, 1, 3, 4, 1, 3, 1, 8, 3, 5, 1, 12, 1, 7, 3, 16, 1, ... . Sequences appearing after division: shifted A144433 or A195161, A064680. For p=3, we have (n+2)^2, -n^2.

%C First column: alternate n^2, 4*(n^2 + n + 1). Its first differences (4, -3, 11, -8, 24, ...) is the sequence of the square array for p=1.

%C Third column: 0, 3, 8, 15, ... is A005563(n).

%C Fifth column: 5, 21, 45, 77, ... is a bisection of A061037(n).

%C Seventh column: 7, 16, 40, 55, 91, 112, ... is a subsequence of A061039(n).

%C Etc. From the Rydberg spectra of the hydrogen atom (mentioned in A261327).

%C Starting for instance from p=-3,at the main antidiagonal,yields:

%C -3: -12, 0, -27, 3, ... see p=3

%C -2: -1, -8, -3, -16, -5, ... p=2

%C -1: -4, 3, -11, 8, -24, 19, ... p=1.

%Y Cf. A000290, A002061, A005563, A061037, A061039, A064680, A112087, A144433, A195161, A261327.

%K sign,tabl

%O 0,3

%A _Paul Curtz_, Jan 05 2017

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Last modified August 11 23:45 EDT 2020. Contains 336434 sequences. (Running on oeis4.)