A239287 Triangle T(n,k), 0 <= k <= n, read by rows: T(n,k) = floor(n/2) - min(k,n-k).

0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 2, 1, 0, 1, 2, 2, 1, 0, 0, 1, 2, 3, 2, 1, 0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 4, 3, 2, 1, 0, 1, 2, 3, 4, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 0, 1, 2

Offset

0,11

Comments

Row sums are A110660(n).

Links

G. C. Greubel, Rows, n=0..100 of triangle, flattened

Formula

T(n,k) = floor(n/2) - min(k,n-k).

Example

Triangle begins:
0;
0, 0;
1, 0, 1;
1, 0, 0, 1;
2, 1, 0, 1, 2;
2, 1, 0, 0, 1, 2;
3, 2, 1, 0, 1, 2, 3;
3, 2, 1, 0, 0, 1, 2, 3;
4, 3, 2, 1, 0, 1, 2, 3, 4;
4, 3, 2, 1, 0, 0, 1, 2, 3, 4;
5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5;
5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5;
6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6;
6, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 6;
7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7;
7, 6, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 6, 7;
8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8;
8, 7, 6, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8;
9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9;
9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9;

Mathematica

Column[Table[Floor[n/2] - Min[k, n - k], {n, 0, 19}, {k, 0, n}]] (* Indranil Ghosh, Mar 15 2017 *)

Prog

(PARI) tabl(nn) = {for(n=0, nn, for(k=0, n, print1(floor(n/2) - min(k, n - k), ", "); ); print(); ); };
tabl(19); \\ Indranil Ghosh, Mar 15 2017
(Python)
i=0
for n in range(0, 20):
....for k in range(0, n+1):
........print str(i)+" "+str((n/2) - min(k, n - k))
........i+=1 # Indranil Ghosh, Mar 15 2017
(Magma) [[Floor(n/2) - Min(k, n-k): k in [0..n]]: n in [0..10]]; // G. C. Greubel, May 26 2018

Crossrefs

Cf. A004526.

Sequence in context: A209318 A170984 A114021 * A305258 A053616 A365746

Adjacent sequences: A239284 A239285 A239286 * A239288 A239289 A239290

Keyword

nonn,tabl

Author

Philippe Deléham, Mar 14 2014

Status

approved