A134226 - OEIS

%I #5 Feb 17 2021 20:24:10

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

%H G. C. Greubel, <a href="/A134226/b134226.txt">Rows n = 1..50 of the triangle, flattened</a>

%F T(n, k) = A134082(n, k) + A002260(n, k) - I, an infinite lower triangular matrix and I = Identity matrix.

%F From _G. C. Greubel_, Feb 17 2021: (Start)

%F T(n, k) = 3*n - 4 if k = n-1 otherwise k.

%F Sum_{k=1..n} T(n, k) = A134227(n) = (n-1)*(n+6)/2 + [n=1]. (End)

%e First few rows of the triangle are:

%e   1;

%e   2, 2;

%e   1, 5, 3;

%e   1, 2, 8,  4;

%e   1, 2, 3, 11,  5;

%e   1, 2, 3,  4, 14,  6;

%e   1, 2, 3,  4,  5, 17, 7;

%e   ...

%t T[n_, k_]:= If[k==n-1, 3*n-4, k];

%t Table[T[n, k], {n,15}, {k,n}]//Flatten (* _G. C. Greubel_, Feb 17 2021 *)

%o (Sage)

%o def A134226(n,k): return 3*n-4 if k==n-1 else k

%o flatten([[A134226(n,k) for k in (1..n)] for n in (1..15)]) # _G. C. Greubel_, Feb 17 2021

%o (Magma)

%o A134226:= func< n,k | k eq n-1 select 3*n-4 else k >;

%o [A134226(n,k): k in [1..n], n in [1..15]]; // _G. C. Greubel_, Feb 17 2021

%Y Cf. A002260, A134082, A134227.

%K nonn,tabl

%O 1,2

%A _Gary W. Adamson_, Oct 14 2007

%E New name and more terms added by _G. C. Greubel_, Feb 17 2021