A267089 - OEIS

%I #15 Jan 12 2016 00:48:50

%S 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,

%T 65,129,66,36,24,24,36,66,129,257,130,68,40,16,40,68,130,257,513,258,

%U 132,72,48,48,72,132,258,513,1025,514,260,136,80,32,80,136,260,514

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

%C Inspired by A137932 and A042948.

%C Conjectures:

%C (i) The first column is A083318.

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

%H Kival Ngaokrajang, <a href="/A267089/a267089.pdf">Illustration of initial terms</a>, <a href="/A267089/a267089_2.pdf">T(n,k) for n = 0..15, k = 0..10</a>

%e See the "Illustration of initial terms" link for explicit examples.

%e Triangle begins:

%e n\k 0   1  2  3  4  5  6   7   8 ...

%e 0   1

%e 1   3   3

%e 2   5   2  5

%e 3   9   6  6  9

%e 4  17  10  4 10 17

%e 5  33  18 12 12 18 33

%e 6  65  34 20  8 20 34 65

%e 7 129  66 36 24 24 36 66 129

%e 8 257 130 68 40 16 40 68 130 257

%e ...

%o (Small Basic)

%o t[0][0] = 1

%o t[1][0] = 3

%o t[1][1] = 3

%o TextWindow.Write("1, 3, 3, ")

%o For n = 2 To 20

%o   For k = 0 To n

%o     If k = 0 Or k = n then

%o       t[n][k] = 1 + math.Power(2,n)

%o     Else

%o       t[n][k] = 2*t[n-2][k-1]

%o     EndIf

%o     TextWindow.Write(t[n][k]+", ")

%o   EndFor

%o Endfor

%Y Cf. A042948, A083318, A086066, A137932.

%K nonn,tabl

%O 0,2

%A _Kival Ngaokrajang_, Jan 10 2016