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A347326
A347738 with rows normalized by subtracting each term in a row from the first term in the row.
2
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
KEYWORD
nonn,tabf
AUTHOR
N. J. A. Sloane, Sep 13 2021
STATUS
approved