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

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, 0, 43, 24, 48, 40, 51, 48, 52, 0, -36, 7, -12, 12, 4, 15, 12, 16, 0, 68, 32, 75, 56, 80, 72, 83, 80, 84, 0, -59, 9, -27

Offset: 0

Author

Paul Curtz, Jan 05 2017

Keywords

• sign
• tabl

Comments

Successive rows:

p

0: 0, 0, 0, 0, 0, 0, 0, ...

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

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

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

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

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

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

... .

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

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.

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.

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

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

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

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

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

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

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

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

Crossrefs

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