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Triangle T(n, k) = (k-1)*(3*n-k-1), read by rows.
1

%I #19 Apr 01 2021 17:27:27

%S 0,0,3,0,6,10,0,9,16,21,0,12,22,30,36,0,15,28,39,48,55,0,18,34,48,60,

%T 70,78,0,21,40,57,72,85,96,105,0,24,46,66,84,100,114,126,136,0,27,52,

%U 75,96,115,132,147,160,171

%N Triangle T(n, k) = (k-1)*(3*n-k-1), read by rows.

%H G. C. Greubel, <a href="/A141434/b141434.txt">Rows n = 1..50 of the triangle, flattened</a>

%F Sum_{k=1..n} T(n,k) = (n-1)*n*(7*n-5)/6. - _R. J. Mathar_, Sep 07 2011

%e Triangle begins as:

%e 0;

%e 0, 3;

%e 0, 6, 10;

%e 0, 9, 16, 21;

%e 0, 12, 22, 30, 36;

%e 0, 15, 28, 39, 48, 55;

%e 0, 18, 34, 48, 60, 70, 78;

%e 0, 21, 40, 57, 72, 85, 96, 105;

%e 0, 24, 46, 66, 84, 100, 114, 126, 136;

%e 0, 27, 52, 75, 96, 115, 132, 147, 160, 171;

%p A141434:= (n,k) -> (k-1)*(3*n-k-1); seq(seq(A141434(n,k), k=1..n), n=1..12); # _G. C. Greubel_, Apr 01 2021

%t Table[(k-1)*(3*n-k-1), {n, 12}, {k, n}]//Flatten (* modified by _G. C. Greubel_, Apr 01 2021 *)

%o (Magma) [(k-1)*(3*n-k-1): k in [1..n], n in [1..12]]; // _G. C. Greubel_, Apr 01 2021

%o (Sage) flatten([[(k-1)*(3*n-k-1) for k in (1..n)] for n in (1..12)]) # _G. C. Greubel_, Apr 01 2021

%Y Cf. A255211 (row sums).

%K nonn,easy,tabl

%O 1,3

%A _Roger L. Bagula_ and _Gary W. Adamson_, Aug 06 2008