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A280579 Square array read by antidiagonals downwards giving the first differences A261327(n+p) - A261327(n), with p >= 0. 1
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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.

LINKS

Table of n, a(n) for n=0..58.

CROSSREFS

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

Sequence in context: A263618 A156788 A130801 * A086165 A301408 A227290

Adjacent sequences:  A280576 A280577 A280578 * A280580 A280581 A280582

KEYWORD

sign,tabl

AUTHOR

Paul Curtz, Jan 05 2017

STATUS

approved

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Last modified July 5 00:40 EDT 2020. Contains 335457 sequences. (Running on oeis4.)