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%I #8 Sep 08 2022 08:45:32
%S 1,2,3,2,6,3,2,9,9,3,2,12,18,12,3,2,15,30,30,15,3,2,18,45,60,45,18,3,
%T 2,21,63,105,105,63,21,3,2,24,84,168,210,168,84,24,3,2,27,108,252,378,
%U 378,252,108,27,3
%N Triangle T(n,k) = A124927(n,k) + A134058(n,k) - A007318(n,k), read by rows.
%H G. C. Greubel, <a href="/A134060/b134060.txt">Rows n = 0..50 of the triangle, flattened</a>
%F T(n,k) = A124927(n,k) + A134058(n,k) - A007318(n,k) as infinite lower triangular matrices.
%F Sum_{k=0..n} T(n, k) = A052940(n).
%F T(n, k) = 3*binomial(n,k) - [k=0] - [n=0]. - _G. C. Greubel_, May 03 2021
%e First few rows of the triangle are:
%e 1;
%e 2, 3;
%e 2, 6, 3;
%e 2, 9, 9, 3;
%e 2, 12, 18, 12, 3;
%e 2, 15, 30, 30, 15, 3;
%e ...
%t Table[3*Binomial[n, k] -Boole[k==0] -Boole[n==0], {n,0,12}, {k,0,n}]//Flatten (* _G. C. Greubel_, May 03 2021 *)
%o (Magma) [1] cat [k eq 0 select 2 else 3*Binomial(n,k): k in [0..n], n in [1..12]]; // _G. C. Greubel_, May 03 2021
%o (Sage)
%o def A134060(n,k): return 3*binomial(n,k) -bool(k==0) -bool(n==0)
%o flatten([[A134060(n,k) for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, May 03 2021
%Y Cf. A007318, A052940 (row sums), A127927, A134058.
%K nonn,tabl
%O 0,2
%A _Gary W. Adamson_, Oct 05 2007
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