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Row sums in A347738 when that sequence is written as a triangle.
1

%I #20 Sep 19 2021 19:28:14

%S 0,2,12,48,167,541,1692,5187,15700,47030,139986,415385,1230417,

%T 3638657,10744058,31705658,93563017,276079102,814408697,2402076923,

%U 7085491321,20902994644,61668276920,181926014930,536710980085,1583529043750,4672393755494,13786612213841

%N Row sums in A347738 when that sequence is written as a triangle.

%C Ratio of successive terms, a(n+1)/a(n), seems to be converging to ~2.9506. - _Michael S. Branicky_, Sep 19 2021

%e Row 2 is 4, 3, 2, 2, 1, 0, which has sum 12.

%t Total /@ TakeList[Import["https://oeis.org/A347738/b347738.txt", "Data"][[All, -1]], {1}~Join~Array[3*2^# &, 13, 0]] (* _Michael De Vlieger_, Sep 13 2021, generated using the b-file at A347738 *)

%o (Python)

%o def afind():

%o num, gte_inventory, rowsum, bigc = 0, [1], 0, 0

%o print(0, end=", ")

%o while True:

%o c = gte_inventory[num] if num <= bigc else 0

%o num += 1

%o rowsum += c

%o if c == 0:

%o print(rowsum, end=", ")

%o num = rowsum = 0

%o for i in range(min(c, bigc)+1):

%o gte_inventory[i] += 1

%o for i in range(bigc+1, c+1):

%o gte_inventory.append(1)

%o bigc = len(gte_inventory) - 1

%o afind() # _Michael S. Branicky_, Sep 19 2021

%Y Cf. A347738, A003945 (row lengths).

%K nonn,hard

%O 0,2

%A _N. J. A. Sloane_, Sep 13 2021

%E a(14)-a(16) from _Michael De Vlieger_, Sep 13 2021

%E a(17)-a(27) from _Michael S. Branicky_, Sep 18 2021