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

Author

N. J. A. Sloane, Sep 13 2021

Keywords

• nonn
• tabf

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.

Examples

			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],
...
		

Links

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

Crossrefs

Cf. A347738.

Programs

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