%I #22 Sep 08 2022 08:45:14
%S 1,0,1,0,0,1,0,0,1,1,0,0,0,4,1,0,0,0,0,10,1,0,0,0,0,1,20,1,0,0,0,0,0,
%T 7,35,1,0,0,0,0,0,0,28,56,1,0,0,0,0,0,0,1,84,84,1,0,0,0,0,0,0,0,10,
%U 210,120,1,0,0,0,0,0,0,0,0,55,462,165,1,0,0,0,0,0,0,0,0,1,220,924,220,1
%N Triangle T(n,k) with diagonals T(n,n-k) = binomial(n,3k).
%C Row sums are A024493.
%C From _R. J. Mathar_, Mar 22 2013: (Start)
%C The matrix inverse starts
%C 1;
%C 0, 1;
%C 0, 0, 1;
%C 0, 0, -1, 1;
%C 0, 0, 4, -4, 1;
%C 0, 0, -40, 40, -10, 1;
%C 0, 0, 796, -796, 199, -20, 1;
%C 0, 0, -27580, 27580, -6895, 693, -35, 1;
%C ... (End)
%H Seiichi Manyama, <a href="/A098172/b098172.txt">Rows n = 0..139, flattened</a>
%F Triangle T(n, k) = binomial(n, 3(n-k)).
%e Rows begin
%e {1},
%e {0,1},
%e {0,0,1},
%e {0,0,1,1},
%e {0,0,0,4,1},
%e {0,0,0,0,10,1},
%e ...
%t Table[Binomial[n, 3(n-k)], {n, 0, 12}, {k, 0, n}]//Flatten (* _G. C. Greubel_, Mar 15 2019 *)
%o (PARI) {T(n, k) = binomial(n, 3*(n-k))}; \\ _G. C. Greubel_, Mar 15 2019
%o (Magma) [[Binomial(n, 3*(n-k)): k in [0..n]]: n in [0..12]]; // _G. C. Greubel_, Mar 15 2019
%o (Sage) [[binomial(n, 3*(n-k)) for k in (0..n)] for n in (0..12)] # _G. C. Greubel_, Mar 15 2019
%o (GAP) Flat(List([0..12], n-> List([0..n], k-> Binomial(n, 3*(n-k)) ))); # _G. C. Greubel_, Mar 15 2019
%Y Cf. A098158.
%K easy,nonn,tabl
%O 0,14
%A _Paul Barry_, Aug 30 2004