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A267090 Triangle read by rows: Fill an n X n square with 1's, except for 0's on the two main diagonals. Then T(n,k) is decimal equivalent of the k-th row (0<=k<=n).

%I A267090 #19 Jan 30 2016 04:35:44
%S A267090 0,0,0,2,5,2,6,9,9,6,14,21,27,21,14,30,45,51,51,45,30,62,93,107,119,
%T A267090 107,93,62,126,189,219,231,231,219,189,126,254,381,443,471,495,471,
%U A267090 443,381,254,510,765,891,951,975,975,951,891,765,510
%N A267090 Triangle read by rows: Fill an n X n square with 1's, except for 0's on the two main diagonals. Then T(n,k) is decimal equivalent of the k-th row (0<=k<=n).
%C A267090 Inspired by A137932 and A042948.
%C A267090 Conjectures:
%C A267090 (i) The first column is A000225/2.
%C A267090 (ii) For even-n, T(n,n/2) = A129868.
%C A267090 (iii) For odd-n, T(n,(n-1)/2) = T(n,(n+1)/2) = A220236.
%H A267090 Kival Ngaokrajang, <a href="/A267090/a267090.pdf">Illustration of initial terms</a>, <a href="/A267090/a267090_1.pdf">T(n,k) for n = 0..10, k = 0..10</a>
%e A267090 Triangle begins:
%e A267090 n\k  0   1   2   3   4   5   6   7   8 ...
%e A267090 0    0
%e A267090 1    0   0
%e A267090 2    2   5   2
%e A267090 3    6   9   9   6
%e A267090 4   14  21  27  21  14
%e A267090 5   30  45  51  51  45  30
%e A267090 6   62  93 107 119 107  93  62
%e A267090 7  126 189 219 231 231 219 189 126
%e A267090 8  254 381 443 471 495 471 443 381 254
%e A267090 ...
%o A267090 (Small Basic)
%o A267090 t[0][0] = 1
%o A267090 t[1][0] = 3
%o A267090 t[1][1] = 3
%o A267090 TextWindow.Write("0, 0, 0, ")
%o A267090 For n = 2 To 20
%o A267090   For k = 0 To n
%o A267090     If k = 0 Or k = n then
%o A267090       t[n][k] = 1 + math.Power(2,n)
%o A267090     Else
%o A267090       t[n][k] = 2*t[n-2][k-1]
%o A267090     EndIf
%o A267090     a = math.Power(2,n+1) -1 -t[n][k]
%o A267090     TextWindow.Write(a+", ")
%o A267090   EndFor
%o A267090 Endfor
%Y A267090 Cf. A000225, A042948, A129868, A137932, A267089.
%K A267090 tabl,nonn
%O A267090 0,4
%A A267090 _Kival Ngaokrajang_, Jan 10 2016