A176149 Triangle T(n, k) = n + 1 - mod(n, k+1) - mod(n, n-k+1), read by rows.

1, 1, 1, 1, 3, 1, 1, 3, 3, 1, 1, 5, 3, 5, 1, 1, 5, 3, 3, 5, 1, 1, 7, 6, 3, 6, 7, 1, 1, 7, 6, 3, 3, 6, 7, 1, 1, 9, 6, 7, 3, 7, 6, 9, 1, 1, 9, 9, 7, 3, 3, 7, 9, 9, 1, 1, 11, 9, 7, 8, 3, 8, 7, 9, 11, 1

Offset

0,5

Comments

Row sums are: 1, 2, 5, 8, 15, 18, 31, 34, 49, 58, 75, ...

Links

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

Formula

T(n, k) = n + 1 - mod(n, k+1) - mod(n, n-k+1).

Example

Triangle begins as:
  1;
  1,  1;
  1,  3, 1;
  1,  3, 3, 1;
  1,  5, 3, 5, 1;
  1,  5, 3, 3, 5, 1;
  1,  7, 6, 3, 6, 7, 1;
  1,  7, 6, 3, 3, 6, 7, 1;
  1,  9, 6, 7, 3, 7, 6, 9, 1;
  1,  9, 9, 7, 3, 3, 7, 9, 9,  1;
  1, 11, 9, 7, 8, 3, 8, 7, 9, 11, 1;

Mathematica

Table[n+1 -Mod[n, k+1] -Mod[n, n-k+1], {n, 0, 10}, {k, 0, n}]//Flatten

Prog

(Sage) flatten([[n+1 - n%(k+1) - n%(n-k+1) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Feb 07 2021
(Magma) [n+1 - n mod (k+1) - n mod (n-k+1): k in [0..n], n in [0..12]]; // G. C. Greubel, Feb 07 2021

Crossrefs

Cf. A176151.

Sequence in context: A152714 A174546 A134444 * A091442 A025834 A257379

Adjacent sequences: A176146 A176147 A176148 * A176150 A176151 A176152

Keyword

nonn,tabl,easy

Author

Roger L. Bagula, Apr 10 2010

Extensions

Edited by G. C. Greubel, Feb 07 2021

Status

approved