A049727 Array T read by diagonals; T(i,j)=number of lattice points in triangle (possibly degenerate) with vertices (0,0),(i,0),(i,j).

1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 6, 5, 5, 6, 6, 7, 7, 6, 6, 7, 7, 9, 10, 9, 7, 7, 8, 8, 10, 11, 11, 10, 8, 8, 9, 9, 12, 13, 15, 13, 12, 9, 9, 10, 10, 13, 16, 16, 16, 16, 13, 10, 10, 11, 11, 15, 17, 19, 21, 19, 17, 15, 11, 11, 12, 12, 16, 19, 21, 22

Offset

0,2

Links

Table of n, a(n) for n=0..71.

Example

 1  2  3  4  5  6  7  8  9 10 11 ...
 2  3  4  5  6  7  8  9 10 11 12 ...
 3  4  6  7  9 10 12 13 15 16 18 ...
 4  5  7 10 11 13 16 17 19 22 23 ...
 5  6  9 11 15 16 19 21 25 26 29 ...
 6  7 10 13 16 21 22 25 28 31 36 ...
 7  8 12 16 19 22 28 29 33 37 40 ...
 8  9 13 17 21 25 29 36 37 41 45 ...
 9 10 15 19 25 28 33 37 45 46 51 ...
10 11 16 22 26 31 37 41 46 55 56 ...
11 12 18 23 29 36 40 45 51 56 66 ...

Maple

A049727 := proc(n, k)
    if n = 0 then
        1+k;
    else
        add(1+floor(k*x/n), x=0..n) ;
    end if;
end proc: # R. J. Mathar, Oct 26 2015

Crossrefs

Sequence in context: A194339 A194335 A026099 * A260690 A060802 A132073

Adjacent sequences: A049724 A049725 A049726 * A049728 A049729 A049730

Keyword

nonn,tabl

Author

Clark Kimberling

Status

approved