A138057 Triangle read by rows: row n consists of 0 followed by n (n+1)'s with alternating signs.
0, 0, -2, 0, -3, 3, 0, -4, 4, -4, 0, -5, 5, -5, 5, 0, -6, 6, -6, 6, -6, 0, -7, 7, -7, 7, -7, 7, 0, -8, 8, -8, 8, -8, 8, -8, 0, -9, 9, -9, 9, -9, 9, -9, 9, 0, -10, 10, -10, 10, -10, 10, -10, 10, -10
Offset: 0
Examples
From _Paolo Xausa_, Nov 10 2023: (Start) Triangle begins: n\k| 0 1 2 3 4 ... ---+--------------------- 0 | 0; 1 | 0, -2; 2 | 0, -3, 3; 3 | 0, -4, 4, -4; 4 | 0, -5, 5, -5, 5; ... (End)
Links
- Paolo Xausa, Table of n, a(n) for n = 0..1325 (rows 0..50 of the triangle, flattened).
Crossrefs
Cf. A131738.
Programs
-
Mathematica
Array[Join[{0},(-1)^Range[#](#+1)]&,15,0] (* Paolo Xausa, Nov 10 2023 *)
Formula
T(n,k) = [k>0]*(n+1)*(-1)^k, with n >= 0 and 0 <= k <= n, where [] is the Iverson bracket. - Paolo Xausa, Nov 10 2023