cp's OEIS Frontend

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

%I A347326 #16 Sep 19 2021 19:26:22
%S A347326 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,
%T A347326 12,13,16,18,19,19,19,20,20,20,20,21,21,21,22,0,4,11,18,22,23,25,26,
%U A347326 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
%N A347326 A347738 with rows normalized by subtracting each term in a row from the first term in the row.
%C A347326 As a result of the normalization, each row starts at 0 and is nondecreasing.
%C A347326 There was a possibility that the new rows would appear to be converging to something, although that is not apparent at present.
%H A347326 Michael S. Branicky, <a href="/A347326/b347326.txt">Table of n, a(n) for n = 0..24573</a> (rows 0 <= k <= 13 when considered as an irregular triangle)
%e A347326 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].
%e A347326 The first few normalized rows are:
%e A347326 [0],
%e A347326 [0, 0, 1],
%e A347326 [0, 1, 2, 2, 3, 4],
%e A347326 [0, 2, 4, 5, 5, 5, 7, 8, 8, 9, 9, 10],
%e A347326 [0, 3, 7, 10, 11, 11, 13, 13, 12, 12, 13, 16, 18, 19, 19, 19, 20, 20, 20, 20, 21, 21, 21, 22],
%e A347326 [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],
%e A347326 ...
%o A347326 (Python)
%o A347326 def aupton(nn):
%o A347326     num, gte_inventory, bigc, row, alst = 0, [1], 0, [], [0]
%o A347326     while len(alst) < nn + 1:
%o A347326         c = gte_inventory[num] if num <= bigc else 0
%o A347326         row.append(c)
%o A347326         num += 1
%o A347326         if c == 0:
%o A347326             num = 0
%o A347326             alst.extend([row[0] - row[i] for i in range(len(row))])
%o A347326             row = []
%o A347326         for i in range(min(c, bigc)+1):
%o A347326             gte_inventory[i] += 1
%o A347326         for i in range(bigc+1, c+1):
%o A347326             gte_inventory.append(1)
%o A347326         bigc = len(gte_inventory) - 1
%o A347326     return alst
%o A347326 print(aupton(92)) # _Michael S. Branicky_, Sep 19 2021
%Y A347326 Cf. A347738.
%K A347326 nonn,tabf
%O A347326 0,7
%A A347326 _N. J. A. Sloane_, Sep 13 2021