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A049801 Triangular array T, read by rows: T(n,k) = n mod floor(k/3), k = 3..n and n >= 3.

%I A049801 #30 Sep 08 2022 08:44:58
%S A049801 0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,
%T A049801 1,1,0,0,0,1,1,1,2,2,2,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,0,0,
%U A049801 0,0,0,0,2,2,2,2,2,2,0,0,0,1,1,1,0,0,0,3,3,3,0
%N A049801 Triangular array T, read by rows: T(n,k) = n mod floor(k/3), k = 3..n and n >= 3.
%H A049801 G. C. Greubel, <a href="/A049801/b049801.txt">Rows n = 3..100 of triangle, flattened</a>
%e A049801 Array T(n,k) (with rows n >= 3 and columns k >= 3) begins as follows:
%e A049801   0;
%e A049801   0, 0;
%e A049801   0, 0, 0;
%e A049801   0, 0, 0, 0;
%e A049801   0, 0, 0, 1, 1;
%e A049801   0, 0, 0, 0, 0, 0;
%e A049801   0, 0, 0, 1, 1, 1, 0;
%e A049801   0, 0, 0, 0, 0, 0, 1, 1;
%e A049801   0, 0, 0, 1, 1, 1, 2, 2, 2;
%e A049801   0, 0, 0, 0, 0, 0, 0, 0, 0, 0;
%e A049801   0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1;
%e A049801   0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2;
%e A049801   ...
%p A049801 # To get the sequence:
%p A049801 seq(seq(n mod floor(k/3), k = 3..n), n = 3..30);
%p A049801 # To get the triangular array:
%p A049801 for n from 3 to 30 do
%p A049801     seq(n mod floor(k/3), k = 3..n);
%p A049801 end do; # _Petros Hadjicostas_, Nov 20 2019
%t A049801 Table[Mod[n, Floor[k/3]], {n,3,15}, {k,3,n}]//Flatten (* _G. C. Greubel_, Dec 09 2019 *)
%o A049801 (PARI) T(n,k) = lift(Mod(n, k\3)); \\ _G. C. Greubel_, Dec 09 2019
%o A049801 (Magma) [ n mod Floor(k/3): k in [3..n], n in [3..15]]; // _G. C. Greubel_, Dec 09 2019
%o A049801 (Sage) [[ mod(n, floor(k/3)) for k in (3..n)] for n in (3..15)] # _G. C. Greubel_, Dec 09 2019
%o A049801 (GAP) Flat(List([3..15], n-> List([3..n], k-> n mod Int(k/3) ))); # _G. C. Greubel_, Dec 09 2019
%Y A049801 Row sums are in A049799.
%Y A049801 Cf. A049797, A049798, A049800.
%K A049801 nonn,tabl
%O A049801 3,43
%A A049801 _Clark Kimberling_
%E A049801 Name edited by and more terms from _Petros Hadjicostas_, Nov 20 2019