A143975 -id:A143975 - cp's OEIS frontend

A183856 n+floor(sqrt(3n-2)); complement of A143975.

2, 4, 5, 7, 8, 10, 11, 12, 14, 15, 16, 17, 19, 20, 21, 22, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74, 75, 76, 77, 78, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 102, 103, 104, 105, 106

Offset: 1

Clark Kimberling, Jan 07 2011

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A000212, A143975.

seq(seq(i+k,i=ceil((k^2+2)/3) .. ((k+1)^2+1)/3),k=1..10); # Robert Israel, Jun 04 2019

Array[#+Floor[Sqrt[3#-2]]&,100] (* Harvey P. Dale, Mar 15 2013 *)

a(n+1) - a(n) = 2 if n is in A000212, 1 otherwise. - Robert Israel, Jun 04 2019

A143974 Rectangular array R by antidiagonals: label each unit square in the first quadrant lattice by its northeast vertex (x,y) and mark those having x+y=1(mod 3); then R(m,n) is the number of marked unit squares in the rectangle [0,m]x[0,n].

Original entry on oeis.org

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

Offset: 1

Clark Kimberling, Sep 06 2008

Diagonals: A000212, A128422, A032765, A143975, A071408.

Rows: A002264, A004523, A000027, A004773, A138235, A005843, A047349 et al.

			Northwest corner:
0 0 1 1 1 2
0 1 2 2 3 4
1 2 3 4 5 6
1 2 4 5 6 8
1 3 5 6 8 10
R(3,4) counts these marked squares: (1,3), (2,2), (3,1), (3,4).

Cf. A143976, A143977.

R(m,n)=floor(mn/3).

cp's OEIS Frontend

A183856 n+floor(sqrt(3n-2)); complement of A143975.

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