A368509 Irregular triangle read by rows. A variation on the inventory sequence A342585. See Comments and Example sections for details.

0, 1, 1, 1, 2, 2, 1, 2, 0, 0, 2, 3, 2, 3, 2, 5, 1, 2, 0, 0, 3, 5, 3, 4, 2, 6, 2, 4, 1, 2, 2, 2, 1, 1, 0, 0, 4, 7, 4, 7, 3, 10, 3, 6, 2, 4, 2, 2, 2, 2, 1, 2, 0, 0, 5, 9, 5, 8, 4, 14, 3, 6, 3, 6, 3, 4, 3, 3, 1, 2, 1, 1, 1, 1, 1, 1, 0, 0, 6, 11, 6, 14, 5, 14, 4, 10, 4, 9, 4, 5

Offset

1,5

Comments

Build an irregular triangle in a slightly similar manner to A342585:

Here, record the number of rows containing zeros thus far in the irregular triangle, then the number of columns containing zeros thus far, then the number of rows containing ones thus far, then again the number of columns with ones and so on alternately counts of rows and of columns, until a completed row-column value pair is recorded with either being zero; a new row of the triangle then starts again, recording the number of rows having any zero in them, then the number of columns, and so on. The sequence is the triangle read by rows.

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Example

The irregular triangle begins:
  0,  1;
  1,  1,  2,  2,  1,  2,  0,  0;
  2,  3,  2,  3,  2,  5,  1,  2,  0,  0;
  3,  5,  3,  4,  2,  6,  2,  4,  1,  2,  2,  2,  1,  1,  0,  0;
  4,  7,  4,  7,  3, 10,  3,  6,  2,  4,  2,  2,  2,  2,  1,  2,  0,  0;
  ...

Prog

(Python)
from itertools import islice
from collections import Counter
def agen(): # generator of terms
    rowinventory, colinventory, thisrow, m = Counter(), dict(), set(), 0
    while True:
        rc = rowinventory[m]
        yield rc
        if rc not in thisrow: rowinventory[rc] += 1; thisrow.add(rc)
        if rc not in colinventory: colinventory[rc] = {2*m}
        else: colinventory[rc].add(2*m)
        cc = len(colinventory.get(m, set()))
        yield cc
        if cc not in thisrow: rowinventory[cc] += 1; thisrow.add(cc)
        if cc not in colinventory: colinventory[cc] = {2*m+1}
        else: colinventory[cc].add(2*m+1)
        if rc == 0 or cc == 0: m = 0; thisrow = set()
        else: m += 1
print(list(islice(agen(), 90))) # Michael S. Branicky, Dec 28 2023

Crossrefs

Cf. A342585.

Sequence in context: A208929 A039965 A300481 * A074942 A043754 A144191

Adjacent sequences: A368506 A368507 A368508 * A368510 A368511 A368512

Keyword

nonn,tabf

Author

Tamas Sandor Nagy, Dec 28 2023

Status

approved