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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.

%I A267089 #15 Jan 12 2016 00:48:50
%S A267089 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 A267089 65,129,66,36,24,24,36,66,129,257,130,68,40,16,40,68,130,257,513,258,
%U A267089 132,72,48,48,72,132,258,513,1025,514,260,136,80,32,80,136,260,514
%N A267089 T(n,k) is decimal conversion of 1's in an n X n table that lie on its principal diagonals.
%C A267089 Inspired by A137932 and A042948.
%C A267089 Conjectures:
%C A267089 (i) The first column is A083318.
%C A267089 (ii) T(n,k) = A086066(m) where m >= 10, n = m - 9*k, k = floor(m/10).
%H A267089 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 A267089 See the "Illustration of initial terms" link for explicit examples.
%e A267089 Triangle begins:
%e A267089 n\k 0   1  2  3  4  5  6   7   8 ...
%e A267089 0   1
%e A267089 1   3   3
%e A267089 2   5   2  5
%e A267089 3   9   6  6  9
%e A267089 4  17  10  4 10 17
%e A267089 5  33  18 12 12 18 33
%e A267089 6  65  34 20  8 20 34 65
%e A267089 7 129  66 36 24 24 36 66 129
%e A267089 8 257 130 68 40 16 40 68 130 257
%e A267089 ...
%o A267089 (Small Basic)
%o A267089 t[0][0] = 1
%o A267089 t[1][0] = 3
%o A267089 t[1][1] = 3
%o A267089 TextWindow.Write("1, 3, 3, ")
%o A267089 For n = 2 To 20
%o A267089   For k = 0 To n
%o A267089     If k = 0 Or k = n then
%o A267089       t[n][k] = 1 + math.Power(2,n)
%o A267089     Else
%o A267089       t[n][k] = 2*t[n-2][k-1]
%o A267089     EndIf
%o A267089     TextWindow.Write(t[n][k]+", ")
%o A267089   EndFor
%o A267089 Endfor
%Y A267089 Cf. A042948, A083318, A086066, A137932.
%K A267089 nonn,tabl
%O A267089 0,2
%A A267089 _Kival Ngaokrajang_, Jan 10 2016