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%I #7 Nov 17 2016 08:03:03
%S 1,2,1,1,2,1,2,1,2,1,1,2,1,2,1,2,1,2,1,2,1,1,2,1,2,1,2,1,2,1,2,1,2,1,
%T 2,1,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1
%N 3*A128174 - 2*A000012(signed).
%C Row sums = A032766, congruent to {0,1} mod 3: (1, 3, 4, 6, 7, 9, 10,...).
%C Sequence array for the expansion of (1+2x)/(1-x^2). A105476 is an eigensequence. [From _Paul Barry_, Nov 03 2010]
%F 3*A128174 - 2*A000012(signed + - + 1 by columns). (1, 2, 1, 2, 1,...) in every column.
%F Triangle T(n,k)=if(k<=n,(3-(-1)^(n-k))/2). [From _Paul Barry_, Nov 03 2010]
%e First few rows of the triangle are:
%e 1;
%e 2, 1;
%e 1, 2, 1;
%e 2, 1, 2, 1;
%e 1, 2, 1, 2, 1;
%e 2, 1, 2, 1, 2, 1;
%e ...
%t T[n_, k_] := Mod[n-k, 2]+1; Table[T[n, k], {n, 1, 10}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Nov 17 2016 *)
%Y Cf. A128174, A000012, A032766.
%K nonn,tabl
%O 1,2
%A _Gary W. Adamson_, Jul 07 2007
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