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

0,8

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.

Links

Table of n, a(n) for n=0..96.

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

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.

Example

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

Prog

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

Crossrefs

Cf. A002262, A052146.

First row with n values: A006893(n).

Sequence in context: A127587 A175832 A330961 * A321223 A082926 A060564

Adjacent sequences: A345233 A345234 A345235 * A345237 A345238 A345239

Keyword

nonn,tabf

Author

John-Vincent Saddic, Jul 14 2021

Status

approved