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A267089
T(n,k) is decimal conversion of 1's in an n X n table that lie on its principal diagonals.
2
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).
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
KEYWORD
nonn,tabl
AUTHOR
Kival Ngaokrajang, Jan 10 2016
STATUS
approved