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A166692 Triangle T(n,k) read by rows: T(n,k) = 2^(k-1), k>0, T(n,0) = (n+1) mod 2.

%I A166692 #16 Apr 24 2023 02:06:24
%S A166692 1,0,1,1,1,2,0,1,2,4,1,1,2,4,8,0,1,2,4,8,16,1,1,2,4,8,16,32,0,1,2,4,8,
%T A166692 16,32,64,1,1,2,4,8,16,32,64,128,0,1,2,4,8,16,32,64,128,256,1,1,2,4,8,
%U A166692 16,32,64,128,256,512,0,1,2,4,8,16,32,64,128,256,512,1024
%N A166692 Triangle T(n,k) read by rows: T(n,k) = 2^(k-1), k>0, T(n,0) = (n+1) mod 2.
%C A166692 Variant of A166918.
%H A166692 G. C. Greubel, <a href="/A166692/b166692.txt">Rows n = 0..100 of the triangle, flattened</a>
%F A166692 T(2n, k) = A011782(k).
%F A166692 T(2n+1, k) = A131577(k).
%F A166692 Sum_{k=0..n} T(n,k) = A051049(n).
%F A166692 From _G. C. Greubel_, Apr 24 2023: (Start)
%F A166692 T(2*n, n) = A011782(n).
%F A166692 Sum_{k=0..n} (-1)^k*T(n, k) = (-1)^n * A005578(n).
%F A166692 Sum_{k=0..n} T(n-k, k) = A106624(n). (End)
%e A166692 Triangle begins as:
%e A166692   1;
%e A166692   0, 1;
%e A166692   1, 1, 2;
%e A166692   0, 1, 2, 4;
%e A166692   1, 1, 2, 4, 8;
%e A166692   0, 1, 2, 4, 8, 16;
%t A166692 Join[{1,0},Flatten[Riffle[Table[2^Range[0,n],{n,0,10}],{1,0}]]] (* _Harvey P. Dale_, Jan 18 2015 *)
%o A166692 (Magma)
%o A166692 A166692:= func< n,k | k eq 0 select ((n+1) mod 2) else 2^(k-1) >;
%o A166692 [A166692(n,k): k in [0..n], n in [0..15]]; // _G. C. Greubel_, Apr 24 2023
%o A166692 (SageMath)
%o A166692 def A166692(n,k): return ((n+1)%2) if (k==0) else 2^(k-1)
%o A166692 flatten([[A166692(n,k) for k in range(n+1)] for n in range(16)]) # _G. C. Greubel_, Apr 24 2023
%Y A166692 Cf. A005578, A011782, A051049, A131577, A106624, A166494, A166918.
%K A166692 nonn,easy,tabl
%O A166692 0,6
%A A166692 _Paul Curtz_, Oct 18 2009
%E A166692 More terms from _Harvey P. Dale_, Jan 18 2015