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A134231 Triangle T(n, k) = n -k +1 with T(n, n-1) = 2*n-1 and T(n, n) = 1, read by rows.

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