A182630 T(n,k) = A002024(k+1)*n + A002262(k), n >= 0, k >= 0, read by antidiagonals.

0, 1, 0, 2, 2, 1, 3, 4, 3, 0, 4, 6, 5, 3, 1, 5, 8, 7, 6, 4, 2, 6, 10, 9, 9, 7, 5, 0, 7, 12, 11, 12, 10, 8, 4, 1, 8, 14, 13, 15, 13, 11, 8, 5, 2, 9, 16, 15, 18, 16, 14, 12, 9, 6, 3, 10, 18, 17, 21, 19, 17, 16, 13, 10, 7, 0

Offset

0,4

Comments

A table of congruences.

See A182631 for another version.

Links

Table of n, a(n) for n=0..65.

Example

Table of congruences:
===============+====+=======+==========+=============+====
           mod |  1 |   2   |     3    |      4      | ...
===============+====+=======+==========+=============+====
  congruent to |  0 |  0  1 |  0  1  2 |  0  1  2  3 | ...
===============+====+=======+==========+=============+====
Array begins:  |  0 |  0  1 |  0  1  2 |  0  1  2  3 | ...
               |  1 |  2  3 |  3  4  5 |  4  5  6  7 | ...
               |  2 |  4  5 |  6  7  8 |  8  9 10 11 | ...
               |  3 |  6  7 |  9 10 11 | 12 13 14 15 | ...
               |  4 |  8  9 | 12 13 14 | 16 17 18 19 | ...
               |  5 | 10 11 | 15 16 17 | 20 21 22 23 | ...
               |  6 | 12 13 | 18 19 20 | 24 25 26 27 | ...
               |  7 | 14 15 | 21 22 23 | 28 29 30 31 | ...
               |  8 | 16 17 | 24 25 26 | 32 33 34 35 | ...
               |  9 | 18 19 | 27 28 29 | 36 37 38 39 | ...
               | 10 | 20 21 | 30 31 32 | 40 41 42 43 | ...

Maple

A002262 := proc(n) n-binomial(floor(1/2+sqrt(2+2*n)), 2) ; end proc:
A002024 := proc(n) ceil((sqrt(1+8*n)-1)/2) ; end proc:
A182630 := proc(n, k) A002024(k+1)*n+A002262(k) ; end proc: # R. J. Mathar, Dec 09 2010

Crossrefs

Columns: A001477, A005483, A005408, A008585, A016777, A016789, A008586, A016813, A016825, A004767.

Rows: A002262, A094727, A182815.

Cf. A182631.

Sequence in context: A186711 A061987 A323899 * A208805 A208514 A179901

Adjacent sequences: A182627 A182628 A182629 * A182631 A182632 A182633

Keyword

nonn,tabl,easy

Author

Omar E. Pol, Dec 06 2010

Status

approved