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A141429 Triangle T(n, k) = (k+1)*(n-k+1), read by rows.

%I A141429 #14 Mar 31 2021 01:29:19
%S A141429 2,4,3,6,6,4,8,9,8,5,10,12,12,10,6,12,15,16,15,12,7,14,18,20,20,18,14,
%T A141429 8,16,21,24,25,24,21,16,9,18,24,28,30,30,28,24,18,10,20,27,32,35,36,
%U A141429 35,32,27,20,11,22,30,36,40,42,42,40,36,30,22,12,24,33,40,45,48,49,48,45,40,33,24,13
%N A141429 Triangle T(n, k) = (k+1)*(n-k+1), read by rows.
%H A141429 G. C. Greubel, <a href="/A141429/b141429.txt">Rows n = 1..50 of the triangle, flattened</a>
%F A141429 T(n, k) = (k+1)*(n-k+1).
%F A141429 T(n, k) = A158823(n+2, k+2).
%F A141429 Sum_{k=1..n} T(n, k) = A005581(n+1).
%e A141429 Triangle begins as:
%e A141429    2;
%e A141429    4,  3;
%e A141429    6,  6,  4;
%e A141429    8,  9,  8,  5;
%e A141429   10, 12, 12, 10,  6;
%e A141429   12, 15, 16, 15, 12,  7;
%e A141429   14, 18, 20, 20, 18, 14,  8;
%e A141429   16, 21, 24, 25, 24, 21, 16,  9;
%e A141429   18, 24, 28, 30, 30, 28, 24, 18, 10;
%e A141429   20, 27, 32, 35, 36, 35, 32, 27, 20, 11;
%p A141429 A141429 := proc(n,k)
%p A141429         (k+1)*(n-k+1) ;
%p A141429 end proc:
%p A141429 seq(seq(A141429(n,m),m=1..n),n=1..14) ; # _R. J. Mathar_, Nov 10 2011
%t A141429 Table[(k+1)*(n-k+1), {n,15}, {k,n}]//Flatten
%o A141429 (Magma) [(k+1)*(n-k+1): k in [1..n], n in [1..15]]; // _G. C. Greubel_, Mar 30 2021
%o A141429 (Sage) flatten([[(k+1)*(n-k+1) for k in (1..n)] for n in (1..15)]) # _G. C. Greubel_, Mar 30 2021
%Y A141429 Cf. A003991, A004247, A005581, A144329, A158823.
%K A141429 nonn,easy,tabl
%O A141429 1,1
%A A141429 _Roger L. Bagula_ and _Gary W. Adamson_, Aug 06 2008
%E A141429 Edited by _G. C. Greubel_, Mar 30 2021