%I #12 Sep 08 2022 08:45:53
%S 1,1,1,1,-2,1,1,-5,-5,1,1,-8,-11,-8,1,1,-11,-17,-17,-11,1,1,-14,-23,
%T -26,-23,-14,1,1,-17,-29,-35,-35,-29,-17,1,1,-20,-35,-44,-47,-44,-35,
%U -20,1,1,-23,-41,-53,-59,-59,-53,-41,-23,1,1,-26,-47,-62,-71,-74,-71,-62,-47
%N T(n,k) = 1 + 3*k*(k - n), triangle read by rows (n >= 0, 0 <= k <= n).
%F T(n,k) = 1 - A000326(n) + A000326(k) + A000326(n-k).
%e Triangle begins:
%e 1;
%e 1, 1;
%e 1, -2, 1:
%e 1, -5, -5, 1;
%e 1, -8, -11, -8, 1;
%e 1, -11, -17, -17, -11, 1;
%e 1, -14, -23, -26, -23, -14, 1;
%e 1, -17, -29, -35, -35, -29, -17, 1;
%e 1, -20, -35, -44, -47, -44, -35, -20, 1;
%e 1, -23, -41, -53, -59, -59, -53, -41, -23, 1;
%e 1, -26, -47, -62, -71, -74, -71, -62, -47, -26, 1;
%e ...
%t a[n_] = n*(3*n - 1)/2; (* A000326 *)
%t t[n_, m_] = 1 - a[n] + a[m] + a[n - m];
%t Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
%t Flatten[%]
%o (Maxima) create_list(1 + 3*k*(k - n), n, 0, 20, k, 0, n); /* _Franck Maminirina Ramaharo_, Nov 25 2018 */
%o (Magma) / * As triangle */ [[1 + 3*k*(k - n): k in [0..n]]: n in [0.. 15]]; // _Vincenzo Librandi_, Nov 26 2018
%Y Cf. A000326, A156070, A156072, A176305, A176306, A176307, A176339, A176344.
%K sign,tabl,easy
%O 0,5
%A _Roger L. Bagula_, Apr 22 2010
%E Edited and name clarified by _Franck Maminirina Ramaharo_, Nov 25 2018
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