A327891 Table of A(n,k) read by antidiagonals, where A(n,1)=n-1; A(n,k) is the number of occurrences of A(n,k-1) in the row up to k-1.

0, 1, 1, 1, 1, 2, 2, 2, 1, 3, 1, 1, 1, 1, 4, 3, 3, 2, 1, 1, 5, 1, 1, 2, 2, 1, 1, 6, 4, 4, 3, 1, 2, 1, 1, 7, 1, 1, 1, 3, 1, 2, 1, 1, 8, 5, 5, 3, 2, 3, 1, 2, 1, 1, 9, 1, 1, 2, 2, 1, 3, 1, 2, 1, 1, 10, 6, 6, 4, 3, 4, 1, 3, 1, 2, 1, 1, 11, 1, 1, 1, 3, 2, 4, 1

Offset

1,6

Comments

The terms of each row are quasi-periodic. Starting with n=3, the period starts at k=((n-1)^2)-1. The period is 2*(n-1) long, and we can find its terms with a simple mod function.

The second row is A158416.

Links

Table of n, a(n) for n=1..85.

Example

Table begins:
  0, 1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 1, 7, 1, 8, ...
  1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 1, 7, 1, 8, 1, ...
  2, 1, 1, 2, 2, 3, 1, 3, 2, 4, 1, 4, 2, 5, 1, 5, ...
  3, 1, 1, 2, 1, 3, 2, 2, 3, 3, 4, 1, 4, 2, 4, 3, ...
  4, 1, 1, 2, 1, 3, 1, 4, 2, 2, 3, 2, 4, 3, 3, 4, ...
  5, 1, 1, 2, 1, 3, 1, 4, 1, 5, 2, 2, 3, 2, 4, 2, ...
  6, 1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 2, 2, 3, 2, ...
  7, 1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 1, 7, 2, 2, ...
  8, 1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 1, 7, 1, 8, ...

Prog

(VBA/Excel)
Sub A327891()
For m = 2 To 40
    For i = 2 To 40
        Cells(m, 1) = m - 2
        Cells(m, 2) = 1
        k = Cells(m, i)
        For j = i - 1 To 1 Step -1
            If k = Cells(m, j) Then
                Cells(m, i + 1) = 1 + Cells(m, j + 1)
                Exit For
            Else
                Cells(m, i + 1) = 1
            End If
        Next j
    Next i
Next m
S = 1
For m = 3 To 40
    For k = m - 2 To 1 Step -1
        n = m - k
        Cells(1, S) = Cells(n, k)
        S = S + 1
    Next k
Next m
End Sub

Crossrefs

The second row is A158416.

Sequence in context: A359812 A308367 A205599 * A265671 A214707 A083039

Adjacent sequences: A327888 A327889 A327890 * A327892 A327893 A327894

Keyword

nonn,tabl

Author

Ali Sada, Oct 02 2019

Status

approved