A049727 - OEIS

%I #9 Aug 14 2024 10:01:21

%S 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,

%T 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,

%U 15,17,19,21,19,17,15,11,11,12,12,16,19,21,22

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

%e  1  2  3  4  5  6  7  8  9 10 11 ...

%e  2  3  4  5  6  7  8  9 10 11 12 ...

%e  3  4  6  7  9 10 12 13 15 16 18 ...

%e  4  5  7 10 11 13 16 17 19 22 23 ...

%e  5  6  9 11 15 16 19 21 25 26 29 ...

%e  6  7 10 13 16 21 22 25 28 31 36 ...

%e  7  8 12 16 19 22 28 29 33 37 40 ...

%e  8  9 13 17 21 25 29 36 37 41 45 ...

%e  9 10 15 19 25 28 33 37 45 46 51 ...

%e 10 11 16 22 26 31 37 41 46 55 56 ...

%e 11 12 18 23 29 36 40 45 51 56 66 ...

%p A049727 := proc(n,k)

%p     if n = 0 then

%p         1+k;

%p     else

%p         add(1+floor(k*x/n),x=0..n) ;

%p     end if;

%p end proc:

%p seq(seq(A049727(d-k,k),k=0..d),d=0..12) ; # _R. J. Mathar_, Oct 26 2015

%Y Cf. A000217 (diagonal).

%K nonn,tabl

%O 0,2

%A _Clark Kimberling_