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A134226 Triangle T(n, k) = 3*n - 4 if k = n-1 otherwise k, read by rows.

%I A134226 #5 Feb 17 2021 20:24:10
%S A134226 1,2,2,1,5,3,1,2,8,4,1,2,3,11,5,1,2,3,4,14,6,1,2,3,4,5,17,7,1,2,3,4,5,
%T A134226 6,20,8,1,2,3,4,5,6,7,23,9,1,2,3,4,5,6,7,8,26,10,1,2,3,4,5,6,7,8,9,29,
%U A134226 11,1,2,3,4,5,6,7,8,9,10,32,12,1,2,3,4,5,6,7,8,9,10,11,35,13
%N A134226 Triangle T(n, k) = 3*n - 4 if k = n-1 otherwise k, read by rows.
%H A134226 G. C. Greubel, <a href="/A134226/b134226.txt">Rows n = 1..50 of the triangle, flattened</a>
%F A134226 T(n, k) = A134082(n, k) + A002260(n, k) - I, an infinite lower triangular matrix and I = Identity matrix.
%F A134226 From _G. C. Greubel_, Feb 17 2021: (Start)
%F A134226 T(n, k) = 3*n - 4 if k = n-1 otherwise k.
%F A134226 Sum_{k=1..n} T(n, k) = A134227(n) = (n-1)*(n+6)/2 + [n=1]. (End)
%e A134226 First few rows of the triangle are:
%e A134226   1;
%e A134226   2, 2;
%e A134226   1, 5, 3;
%e A134226   1, 2, 8,  4;
%e A134226   1, 2, 3, 11,  5;
%e A134226   1, 2, 3,  4, 14,  6;
%e A134226   1, 2, 3,  4,  5, 17, 7;
%e A134226   ...
%t A134226 T[n_, k_]:= If[k==n-1, 3*n-4, k];
%t A134226 Table[T[n, k], {n,15}, {k,n}]//Flatten (* _G. C. Greubel_, Feb 17 2021 *)
%o A134226 (Sage)
%o A134226 def A134226(n,k): return 3*n-4 if k==n-1 else k
%o A134226 flatten([[A134226(n,k) for k in (1..n)] for n in (1..15)]) # _G. C. Greubel_, Feb 17 2021
%o A134226 (Magma)
%o A134226 A134226:= func< n,k | k eq n-1 select 3*n-4 else k >;
%o A134226 [A134226(n,k): k in [1..n], n in [1..15]]; // _G. C. Greubel_, Feb 17 2021
%Y A134226 Cf. A002260, A134082, A134227.
%K A134226 nonn,tabl
%O A134226 1,2
%A A134226 _Gary W. Adamson_, Oct 14 2007
%E A134226 New name and more terms added by _G. C. Greubel_, Feb 17 2021