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%I #5 Feb 17 2021 20:24:23
%S 1,3,1,3,5,1,4,3,7,1,5,4,3,9,1,6,5,4,3,11,1,7,6,5,4,3,13,1,8,7,6,5,4,
%T 3,15,1,9,8,7,6,5,4,3,17,1,10,9,8,7,6,5,4,3,19,1,11,10,9,8,7,6,5,4,3,
%U 21,1,12,11,10,9,8,7,6,5,4,3,23,1,13,12,11,10,9,8,7,6,5,4,3,25,1
%N Triangle T(n, k) = n -k +1 with T(n, n-1) = 2*n-1 and T(n, n) = 1, read by rows.
%H G. C. Greubel, <a href="/A134231/b134231.txt">Rows n = 1..50 of the triangle, flattened</a>
%F T(n, k) = A004736(n, k) + A134081(n, k) - I, an infinite lower triangular matrix, where I = Identity matrix.
%F From _G. C. Greubel_, Feb 17 2021: (Start)
%F T(n, k) = n - k + 1 with T(n, n-1) = 2*n - 1 and T(n, n) = 1.
%F Sum_{k=1..n} T(n, k) = (n-1)*(n+6)/2 + [n=1] = A134227(n). (End)
%e First few rows of the triangle are:
%e 1;
%e 3, 1;
%e 3, 5, 1;
%e 4, 3, 7, 1;
%e 5, 4, 3, 9, 1;
%e 6, 5, 4, 3, 11, 1;
%e 7, 6, 5, 4, 3, 13, 1;
%e ...
%t T[n_, k_]:= If[k==n, 1, If[k==n-1, 2*n-1, n-k+1]];
%t Table[T[n, k], {n,15}, {k,n}]//Flatten (* _G. C. Greubel_, Feb 17 2021 *)
%o (Sage)
%o def A134231(n,k): return 1 if k==n else 2*n-1 if k==n-1 else n-k+1
%o flatten([[A134231(n,k) for k in (1..n)] for n in (1..15)]) # _G. C. Greubel_, Feb 17 2021
%o (Magma)
%o A134231:= func< n,k | k eq n select 1 else k eq n-1 select 2*n-1 else n-k+1 >;
%o [A134231(n,k): k in [1..n], n in [1..15]]; // _G. C. Greubel_, Feb 17 2021
%Y Cf. A004736, A134081, A134227.
%K nonn,tabl
%O 1,2
%A _Gary W. Adamson_, Oct 14 2007
%E More terms and title changed by _G. C. Greubel_, Feb 17 2021
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