cp's OEIS Frontend

A176625 T(n,k) = 1 + 3*k*(k - n), triangle read by rows (n >= 0, 0 <= k <= n).

%I A176625 #12 Sep 08 2022 08:45:53
%S A176625 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 A176625 -26,-23,-14,1,1,-17,-29,-35,-35,-29,-17,1,1,-20,-35,-44,-47,-44,-35,
%U A176625 -20,1,1,-23,-41,-53,-59,-59,-53,-41,-23,1,1,-26,-47,-62,-71,-74,-71,-62,-47
%N A176625 T(n,k) = 1 + 3*k*(k - n), triangle read by rows (n >= 0, 0 <= k <= n).
%F A176625 T(n,k) = 1 - A000326(n) + A000326(k) + A000326(n-k).
%e A176625 Triangle begins:
%e A176625   1;
%e A176625   1,   1;
%e A176625   1,  -2,   1:
%e A176625   1,  -5,  -5,   1;
%e A176625   1,  -8, -11,  -8,   1;
%e A176625   1, -11, -17, -17, -11,   1;
%e A176625   1, -14, -23, -26, -23, -14,   1;
%e A176625   1, -17, -29, -35, -35, -29, -17,   1;
%e A176625   1, -20, -35, -44, -47, -44, -35, -20,   1;
%e A176625   1, -23, -41, -53, -59, -59, -53, -41, -23,  1;
%e A176625   1, -26, -47, -62, -71, -74, -71, -62, -47, -26, 1;
%e A176625   ...
%t A176625 a[n_] = n*(3*n - 1)/2; (* A000326 *)
%t A176625 t[n_, m_] = 1 - a[n] + a[m] + a[n - m];
%t A176625 Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
%t A176625 Flatten[%]
%o A176625 (Maxima) create_list(1 + 3*k*(k - n), n, 0, 20, k, 0, n); /* _Franck Maminirina Ramaharo_, Nov 25 2018 */
%o A176625 (Magma) / * As triangle */ [[1 + 3*k*(k - n): k in [0..n]]: n in [0.. 15]];  // _Vincenzo Librandi_, Nov 26 2018
%Y A176625 Cf. A000326, A156070, A156072, A176305, A176306, A176307, A176339, A176344.
%K A176625 sign,tabl,easy
%O A176625 0,5
%A A176625 _Roger L. Bagula_, Apr 22 2010
%E A176625 Edited and name clarified by _Franck Maminirina Ramaharo_, Nov 25 2018