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A049800 Triangular array T, read by rows: T(n,k) = (n+1) mod floor((k+1)/2), k = 1..n and n >= 1.

%I A049800 #27 Sep 08 2022 08:44:58
%S A049800 0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0,2,2,0,0,0,1,1,0,0,
%T A049800 1,1,0,0,0,0,1,1,2,2,0,0,0,1,1,2,2,3,3,1,1,0,0,0,0,0,0,0,0,2,2,0,0,0,
%U A049800 1,1,1,1,1,1,3,3,1,1,0,0,0,0,2,2,2,2,4,4,2,2,0
%N A049800 Triangular array T, read by rows: T(n,k) = (n+1) mod floor((k+1)/2), k = 1..n and n >= 1.
%H A049800 G. C. Greubel, <a href="/A049800/b049800.txt">Rows n = 1..100 of triangle, flattened</a>
%e A049800 Array T(n,k) (with rows n >= 1 and columns k >= 1) begins as follows:
%e A049800   0;
%e A049800   0, 0;
%e A049800   0, 0, 0;
%e A049800   0, 0, 1, 1;
%e A049800   0, 0, 0, 0, 0;
%e A049800   0, 0, 1, 1, 1, 1;
%e A049800   0, 0, 0, 0, 2, 2, 0;
%e A049800   0, 0, 1, 1, 0, 0, 1, 1;
%e A049800   0, 0, 0, 0, 1, 1, 2, 2, 0;
%e A049800   0, 0, 1, 1, 2, 2, 3, 3, 1, 1;
%e A049800   0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0;
%e A049800   ...
%p A049800 # To get the sequence:
%p A049800 seq(seq((n+1) mod floor((k+1)/2), k = 1..n), n = 1..30);
%p A049800 # To get the triangular array:
%p A049800 for n from 1 to 30 do
%p A049800     seq((n+1) mod floor((k+1)/2), k = 1..n);
%p A049800 end do; # _Petros Hadjicostas_, Nov 20 2019
%t A049800 Table[Mod[n+1, Floor[(k+1)/2]], {n,15}, {k,n}]//Flatten (* _G. C. Greubel_, Dec 09 2019 *)
%o A049800 (PARI) T(n,k) = lift(Mod(n+1,(k+1)\2));
%o A049800 for(n=1, 15, for(k=1, n, print1(T(n,k), ", "))) \\ _G. C. Greubel_, Dec 09 2019
%o A049800 (Magma) [ (n+1) mod Floor((k+1)/2): k in [1..n], n in [1..15]]; // _G. C. Greubel_, Dec 09 2019
%o A049800 (Sage) [[ mod(n+1, floor((k+1)/2)) for k in (1..n)] for n in (1..15)] # _G. C. Greubel_, Dec 09 2019
%o A049800 (GAP) Flat(List([1..15], n-> List([1..n], k-> (n+1) mod Int((k+1)/2) ))); # _G. C. Greubel_, Dec 09 2019
%Y A049800 One-half the row sums are in A049798.
%Y A049800 Cf. A049799, A049801.
%K A049800 nonn,tabl
%O A049800 1,26
%A A049800 _Clark Kimberling_
%E A049800 Name edited by _Petros Hadjicostas_, Nov 20 2019