A349042 - OEIS

A349042

Triangle read by rows in which row n >= 1 lists the count of 0's, ..., k's in all previous terms in the triangle. T(0,0) = 0, k is from [0..A049820(n)].

0, 1, 1, 1, 3, 1, 4, 1, 5, 0, 1, 2, 6, 1, 2, 7, 2, 1, 1, 1, 2, 10, 4, 1, 2, 2, 11, 6, 1, 2, 1, 2, 2, 13, 9, 1, 2, 1, 2, 2, 15, 12, 1, 2, 1, 2, 1, 0, 1, 3, 19, 14, 2, 2, 1, 2, 3, 20, 17, 3, 2, 1, 2, 1, 0, 1, 1, 1, 4, 25, 19, 4, 4, 1, 2, 1, 0, 1, 1, 5, 29, 20, 4, 6, 2, 3, 1, 0, 1, 1, 1

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,5

COMMENTS

For n >= 1 the n-th row length equals A049820(n) + 1. The same definition, but for k from [0..n] gives A032531.

LINKS

Table of n, a(n) for n=0..90.

Michael De Vlieger, Scatterplot of a(n) for n=0..31686, i.e., rows 0..256.

Michael De Vlieger, Scatterplot of a(n)for n=0..518562, i.e., rows 0..1024

Index entries for sequences related to the inventory sequence

EXAMPLE

Triangle begins:

k=0 1 2 3 4 5

n=0: 0;

n=1: 1;

n=2: 1;

n=3: 1, 3;

n=4: 1, 4;

n=5: 1, 5, 0, 1;

n=6: 2, 6, 1;

n=7: 2, 7, 2, 1, 1, 1;

MATHEMATICA

c[_] = 0; Reap[Do[w = {}; Array[(Set[m, c[#]]; c[m]++; AppendTo[w, m]) &, If[n == 0, 1, n - DivisorSigma[0, n] + 1], 0]; Sow[w], {n, 0, 15}]][[-1, -1]] // Flatten (* Michael De Vlieger, Nov 09 2021 *)

PROG

(Python)

from collections import Counter

from sympy import divisor_count

def auptor(rows):

alst, inventory = [0], Counter([0])

for m in range(1, rows):

for k in range(m-divisor_count(m)+1):

c = inventory[k]; alst.append(c); inventory.update([c])

return alst

print(auptor(16)) # Michael S. Branicky, Nov 07 2021

CROSSREFS