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A279891 Triangle read by rows, T(n,k) = 2*n, with n>=k>=0.

%I A279891 #40 Oct 09 2018 15:47:28
%S A279891 0,2,2,4,4,4,6,6,6,6,8,8,8,8,8,10,10,10,10,10,10,12,12,12,12,12,12,12,
%T A279891 14,14,14,14,14,14,14,14,16,16,16,16,16,16,16,16,16,18,18,18,18,18,18,
%U A279891 18,18,18,18,20,20,20,20,20,20,20,20,20,20,20,22,22,22,22,22,22,22,22,22,22,22,22
%N A279891 Triangle read by rows, T(n,k) = 2*n, with n>=k>=0.
%C A279891 2*n appears n+1 times in row n.
%F A279891 a(n) = 2*floor((sqrt(1+8*n)-1)/2).
%F A279891 a(n) = 2*A003056(n) = 2*(A002024(n+1)-1).
%e A279891 Triangle begins:
%e A279891 0;
%e A279891 2,  2;
%e A279891 4,  4,  4;
%e A279891 6,  6,  6,  6;
%e A279891 8,  8,  8,  8,  8;
%e A279891 10, 10, 10, 10, 10, 10;
%e A279891 12, 12, 12, 12, 12, 12, 12;
%e A279891 14, 14, 14, 14, 14, 14, 14, 14;
%e A279891 16, 16, 16, 16, 16, 16, 16, 16, 16;
%e A279891 18, 18, 18, 18, 18, 18, 18, 18, 18, 18;
%e A279891 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20;
%e A279891 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22;
%e A279891 ...
%t A279891 Table[ConstantArray[2 n, n + 1], {n, 0, 11}] // Flatten (* _Michael De Vlieger_, Dec 22 2016 *)
%t A279891 Table[#,#/2+1]&/@(2*Range[0,20])//Flatten(* _Harvey P. Dale_, Oct 09 2018 *)
%o A279891 (PARI) row(n) = vector(n, x, 2*(n-1))
%o A279891 trianglerows(n) = for(k=1, n, print(row(k)))
%o A279891 /* Print initial 12 rows of triangle as follows: */
%o A279891 trianglerows(12) \\ _Felix Fröhlich_, Dec 22 2016
%Y A279891 Twice A003056.
%Y A279891 Row sums give A046092.
%Y A279891 Where records occur gives A000217.
%Y A279891 Column 0, and the right border: A005843.
%Y A279891 Also row lengths of the following triangles: A237593, A262045, A262048, A279693.
%Y A279891 Cf. A002024.
%K A279891 nonn,tabl,easy
%O A279891 0,2
%A A279891 _Omar E. Pol_, Dec 22 2016