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

Author

Omar E. Pol, Dec 06 2010

Keywords

• nonn
• tabl
• easy

Comments

A table of congruences.

See A182631 for another version.

Examples

			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 | ...
		

Crossrefs

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

Rows: A002262, A094727, A182815.

Cf. A182631.

Programs

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