A347326 A347738 with rows normalized by subtracting each term in a row from the first term in the row.

0, 0, 0, 1, 0, 1, 2, 2, 3, 4, 0, 2, 4, 5, 5, 5, 7, 8, 8, 9, 9, 10, 0, 3, 7, 10, 11, 11, 13, 13, 12, 12, 13, 16, 18, 19, 19, 19, 20, 20, 20, 20, 21, 21, 21, 22, 0, 4, 11, 18, 22, 23, 25, 26, 25, 25, 27, 29, 30, 30, 29, 28, 28, 29, 31, 33, 35, 36, 39, 40, 41, 42, 42, 42, 42, 43, 43, 43, 43, 43, 43, 43, 44, 44, 44, 44, 44, 44, 44, 45, 45, 45, 45, 46

Offset

0,7

Comments

As a result of the normalization, each row starts at 0 and is nondecreasing.

There was a possibility that the new rows would appear to be converging to something, although that is not apparent at present.

Links

Michael S. Branicky, Table of n, a(n) for n = 0..24573 (rows 0 <= k <= 13 when considered as an irregular triangle)

Example

Row 2 of A347738 is [4,3,2,2,1,0], and subtracting each term from the first term, 4, we get row 2 of the present sequence, [0, 1, 2, 2, 3, 4].
The first few normalized rows are:
[0],
[0, 0, 1],
[0, 1, 2, 2, 3, 4],
[0, 2, 4, 5, 5, 5, 7, 8, 8, 9, 9, 10],
[0, 3, 7, 10, 11, 11, 13, 13, 12, 12, 13, 16, 18, 19, 19, 19, 20, 20, 20, 20, 21, 21, 21, 22],
[0, 4, 11, 18, 22, 23, 25, 26, 25, 25, 27, 29, 30, 30, 29, 28, 28, 29, 31, 33, 35, 36, 39, 40, 41, 42, 42, 42, 42, 43, 43, 43, 43, 43, 43, 43, 44, 44, 44, 44, 44, 44, 44, 45, 45, 45, 45, 46],
...

Prog

(Python)
def aupton(nn):
    num, gte_inventory, bigc, row, alst = 0, [1], 0, [], [0]
    while len(alst) < nn + 1:
        c = gte_inventory[num] if num <= bigc else 0
        row.append(c)
        num += 1
        if c == 0:
            num = 0
            alst.extend([row[0] - row[i] for i in range(len(row))])
            row = []
        for i in range(min(c, bigc)+1):
            gte_inventory[i] += 1
        for i in range(bigc+1, c+1):
            gte_inventory.append(1)
        bigc = len(gte_inventory) - 1
    return alst
print(aupton(92)) # Michael S. Branicky, Sep 19 2021

Crossrefs

Cf. A347738.

Sequence in context: A205958 A309090 A091048 * A071478 A071477 A071507

Adjacent sequences: A347323 A347324 A347325 * A347327 A347328 A347329

Keyword

nonn,tabf

Author

N. J. A. Sloane, Sep 13 2021

Status

approved