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%I #25 Jan 21 2024 05:51:16
%S 0,-1,0,-1,2,0,1,10,12,0,7,30,44,40,0,21,74,116,136,112,0,51,166,268,
%T 344,368,288,0,113,354,580,776,912,928,704,0,239,734,1212,1656,2032,
%U 2272,2240,1664,0,493,1498,2484,3432,4304,5024,5440,5248,3840,0
%N Triangle read by rows: T(n, k) = 2^(n-1)*(2*k - 1) - 2^(k-1)*(2*n - 1).
%H G. C. Greubel, <a href="/A123002/b123002.txt">Rows n = 1..50 of the triangle, flattened</a>
%F T(n, k) = 2^(n-1)*(2*k - 1) - 2^(k-1)*(2*n - 1).
%F Sum_{k=1..n} T(n, k) = 2^(n-1)*(n^2 - 4*n + 2) + (2*n - 1). - _G. C. Greubel_, Jul 14 2021
%e Triangle begins as:
%e 0;
%e -1, 0;
%e -1, 2, 0;
%e 1, 10, 12, 0;
%e 7, 30, 44, 40, 0;
%e 21, 74, 116, 136, 112, 0;
%t T[n_, k_]:= 2^(n-1)*(2*k-1) -2^(k-1)*(2*n-1);
%t Table[T[n, k], {n, 12}, {k, n}]//Flatten
%o (Magma) [2^(n-1)*(2*k-1) -2^(k-1)*(2*n-1): k in [1..n], n in [1..12]]; // _G. C. Greubel_, Jul 14 2021
%o (Sage) flatten([[2^(n-1)*(2*k-1) -2^(k-1)*(2*n-1) for k in (1..n)] for n in (1..12)]) # _G. C. Greubel_, Jul 14 2021
%K sign,tabl
%O 1,5
%A _Roger L. Bagula_, Sep 23 2006
%E Edited by _N. J. A. Sloane_, Oct 01 2006
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