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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).
2
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
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:
seq(seq(A049727(d-k, k), k=0..d), d=0..12) ; # R. J. Mathar, Oct 26 2015
CROSSREFS
Cf. A000217 (diagonal).
Sequence in context: A194339 A194335 A026099 * A260690 A060802 A132073
KEYWORD
nonn,tabl
STATUS
approved