A319080 Sequence, read by rows, encoding an infinite sequence of diamond-shaped arrays of nonnegative integers (see example).

0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 2, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 2, 1, 0, 0, 1, 2, 3, 2, 1, 0, 0, 1, 2, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 2, 1, 0, 0, 1, 2, 3, 2, 1, 0, 0, 1, 2, 3, 4, 3, 2, 1, 0, 0, 1, 2, 3, 2, 1, 0, 0, 1, 2, 1, 0, 0, 1, 0, 0

Offset

0,13

Comments

The sum of each figure corresponds to A005900;

Figure 1:

0 = 0;

Figure 2:

0+0+1+0+0 = 1;

Figure 3:

0+0+1+0+0+1+2+1+0+0+1+0+0 = 6;

Figure n:

0+0+1+0+0+1+2+1+0+...+n+...0+1+2+1+0+0+1+0+0 = A005900(n).

Links

Table of n, a(n) for n=0..84.

Example

Figure 1 has just 0. Figure 2 would look like a 1 surrounded by 0's. Figure 3 would look like a 2 surrounded by 1's surrounded by 0's, etc.
Read by rows, the sequence starts:
Figure 1: 0;
                     0
Figure 2: 0, 0, 1, 0, 0;
                     0
                   0 1 0
                     0
Figure 3: 0, 0, 1, 0, 0, 1, 2, 1, 0, 0, 1, 0, 0;
                     0
                   0 1 0
                 0 1 2 1 0
                   0 1 0
                     0
Figure 4: 0, 0, 1, 0, 0, 1, 2, 1, 0, 0, 1, 2, 3, 2, 1, 0, 0, 1, 2, 1, 0, 0, 1, 0, 0;
                     0
                   0 1 0
                 0 1 2 1 0
               0 1 2 3 2 1 0
                 0 1 2 1 0
                   0 1 0
                     0
...

Mathematica

f[n_] := Join[#, Rest@ Reverse@ #] &@ Range[0, n]; Array[Flatten[f /@ f@ #] &, 5, 0] // Flatten (* Michael De Vlieger, Sep 10 2018 *)

Crossrefs

Cf. A001477, A005900.

Sequence in context: A115079 A286562 A185644 * A025435 A304685 A186714

Adjacent sequences: A319077 A319078 A319079 * A319081 A319082 A319083

Keyword

nonn,tabf

Author

Kritsada Moomuang, Sep 09 2018

Status

approved