A207260 Triangle read by rows: T(n,k) = k^2 + (1-(-1)^(n-k))/2.
0, 1, 1, 0, 2, 4, 1, 1, 5, 9, 0, 2, 4, 10, 16, 1, 1, 5, 9, 17, 25, 0, 2, 4, 10, 16, 26, 36, 1, 1, 5, 9, 17, 25, 37, 49, 0, 2, 4, 10, 16, 26, 36, 50, 64, 1, 1, 5, 9, 17, 25, 37, 49, 65, 81, 0, 2, 4, 10, 16, 26, 36, 50, 64, 82, 100, 1, 1, 5, 9, 17, 25, 37, 49, 65, 81, 101, 121
Offset: 0
Examples
Triangle begins: 0; 1, 1; 0, 2, 4; 1, 1, 5, 9; 0, 2, 4, 10, 16; 1, 1, 5, 9, 17, 25; 0, 2, 4, 10, 16, 26, 36; 1, 1, 5, 9, 17, 25, 37, 49; 0, 2, 4, 10, 16, 26, 36, 50, 64; 1, 1, 5, 9, 17, 25, 37, 49, 65, 81; ...
Links
- Paolo Xausa, Table of n, a(n) for n = 0..11475 (rows 0..150 of triangle, flattened).
Crossrefs
Programs
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Magma
/* As triangle */ [[ k^2 + (1-(-1)^(n-k))/2: k in [0..n]]: n in [0.. 15]]; // Vincenzo Librandi, Nov 09 2024
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Mathematica
Table[k^2 + (1-(-1)^(n-k))/2, {n, 0, 15}, {k, 0, n}] (* Paolo Xausa, Nov 13 2024 *)
Formula
T(n+k, n) = A002522(n) if k is odd.
T(n+k, n) = n^2 = A000290(n) if k is even.
T(2*n, n) = A137928(n), n>0.
T(2*n+1, n+1) = A080335(n).
T(n,0) = A000035(n).
T(n+1,1) = A000034(n).
T(n+2,2) = A010710(n).
T(n+3,3) = A010735(n).
for x = -1, 0, 1 respectively.
G.f.: x*(1 + y - x*y + x*(1 + 2*x)*y^2)/((1 - x^2)*(1 - x*y)^3). - Stefano Spezia, Nov 12 2024
Comments