A235337 Number of integer lattice points inside the square ABCD with side length n>0 with A(-n*sqrt(2)/2| 0), B(n*sqrt(2)/2| 0), C(0| n*sqrt(2)/2) and D(-n*sqrt(2)/2| 0).

1, 5, 13, 13, 25, 41, 41, 61, 85, 113, 113, 145, 181, 181, 221, 265, 313, 313, 365, 421, 421, 481, 545, 545, 613, 685, 761, 761, 841, 925, 925, 1013, 1105, 1201, 1201, 1301, 1405, 1405, 1513, 1625, 1625, 1741, 1861, 1985, 1985, 2113, 2245, 2245, 2381, 2521

Offset

1,2

Links

Reiner Moewald and Vincenzo Librandi, Table of n, a(n) for n = 1..1000 (first 500 terms from Reiner Moewald)

Formula

a(n) := 2*z^2-2*z+1, where z = ceiling(n*sqrt(2)/2). - Giovanni Resta, Jan 10 2014

Mathematica

a[n_] := Block[{z = Ceiling[Sqrt[2]*n/2]}, 1-2*z+2*z^2]; Array[a, 50] (* Giovanni Resta, Jan 10 2014 *)

Crossrefs

Sequence in context: A051899 A085956 A232610 * A151994 A321992 A231806

Adjacent sequences: A235334 A235335 A235336 * A235338 A235339 A235340

Keyword

nonn

Author

Reiner Moewald, Jan 06 2014

Status

approved