A267089 T(n,k) is decimal conversion of 1's in an n X n table that lie on its principal diagonals.

1, 3, 3, 5, 2, 5, 9, 6, 6, 9, 17, 10, 4, 10, 17, 33, 18, 12, 12, 18, 33, 65, 34, 20, 8, 20, 34, 65, 129, 66, 36, 24, 24, 36, 66, 129, 257, 130, 68, 40, 16, 40, 68, 130, 257, 513, 258, 132, 72, 48, 48, 72, 132, 258, 513, 1025, 514, 260, 136, 80, 32, 80, 136, 260, 514

Offset

0,2

Comments

Inspired by A137932 and A042948.

Conjectures:

(i) The first column is A083318.

(ii) T(n,k) = A086066(m) where m >= 10, n = m - 9*k, k = floor(m/10).

Links

Table of n, a(n) for n=0..64.

Kival Ngaokrajang, Illustration of initial terms, T(n,k) for n = 0..15, k = 0..10

Example

See the "Illustration of initial terms" link for explicit examples.
Triangle begins:
n\k 0   1  2  3  4  5  6   7   8 ...
0   1
1   3   3
2   5   2  5
3   9   6  6  9
4  17  10  4 10 17
5  33  18 12 12 18 33
6  65  34 20  8 20 34 65
7 129  66 36 24 24 36 66 129
8 257 130 68 40 16 40 68 130 257
...

Prog

(Small Basic)
t[0][0] = 1
t[1][0] = 3
t[1][1] = 3
TextWindow.Write("1, 3, 3, ")
For n = 2 To 20
  For k = 0 To n
    If k = 0 Or k = n then
      t[n][k] = 1 + math.Power(2, n)
    Else
      t[n][k] = 2*t[n-2][k-1]
    EndIf
    TextWindow.Write(t[n][k]+", ")
  EndFor
Endfor

Crossrefs

Cf. A042948, A083318, A086066, A137932.

Sequence in context: A348298 A101777 A204154 * A016555 A214745 A015909

Adjacent sequences: A267086 A267087 A267088 * A267090 A267091 A267092

Keyword

nonn,tabl

Author

Kival Ngaokrajang, Jan 10 2016

Status

approved