A345236 Triangle read by rows: The rightmost column contains the terms of A002262 starting at A002262(1). Each time a column's value is zero (except for a(0)), the column to its left starts at the next term in A002262, or if that column does not yet exist, it starts at A002262(2).

0, 1, 1, 0, 1, 1, 1, 2, 1, 0, 0, 1, 0, 1, 1, 0, 2, 1, 0, 3, 1, 1, 0, 1, 1, 1, 1, 1, 2, 1, 1, 3, 1, 1, 4, 1, 2, 0, 1, 2, 1, 1, 2, 2, 1, 2, 3, 1, 2, 4, 1, 2, 5, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 2, 1, 0, 0, 3, 1, 0, 0, 4, 1, 0, 0, 5, 1, 0, 0, 6, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 2, 1, 0, 1, 3

Offset: 0

Author

John-Vincent Saddic, Jul 14 2021

Keywords

• nonn
• tabf

Comments

The first row with k columns is the A006893(k)-th. The last row with k columns comprises the first k terms of A006893.

Examples

			Triangle begins as:
  0
  1
  1 0
  1 1
  1 2
  1 0 0
  1 0 1
  1 0 2
  1 0 3
  1 1 0
		

Links

• John-Vincent Saddic, Java code to print the n-th row of the triangle

Crossrefs

Cf. A002262, A052146.

First row with n values: A006893(n).

Programs

Java

See Links. Rows are printed with values concatenated. Values greater than 10 are represented between parentheses, e.g., row 100 is 113(10).

Formula

To calculate the values of the n-th row:

c(m) = floor((sqrt(9 + 8*m) - 3)/2) = A052146(m+1).

r(m) = m - (c(m)^2)/2 - 3*c(m)/2 = A002262(m+1).

The last value of row m is r(m), the second to last value is r(c(m)), the third to last value is r(c(c(m))), and so on until c(m) equals 0.