A111746 - OEIS

%I #12 Sep 08 2022 08:45:21

%S 0,5,17,42,82,143,227,340,484,665,885,1150,1462,1827,2247,2728,3272,

%T 3885,4569,5330,6170,7095,8107,9212,10412,11713,13117,14630,16254,

%U 17995,19855,21840,23952,26197,28577,31098,33762,36575,39539,42660,45940

%N Number of squares in the interior of the square with vertices (n,0), (0,n), (-n,0) and (0,-n) in a square (x,y)-grid.

%F a(n) = n*(4*n^2 + 12*n + 11)/6 + 1/4 - (-1)^n/4 = floor(A000447(n+1)/2).

%F a(n) = 4*A002623(n-1) + A000330(n), with A002623(-1)=0. - _Luce ETIENNE_, May 12 2015

%F G.f.: x*(5 + 2*x + x^2)/((1-x)^4*(1+x)). - _Vincenzo Librandi_, May 12 2015

%p seq(n*(4*n^2-1)/6 - 1/4 + 1/4*(-1)^n,n=1..50);

%t Table[n (4 n^2 + 12 n + 11)/6 + 1/4 - (-1)^n/4, {n, 0, 60}] (* _Vincenzo Librandi_, May 12 2015 *)

%o (Magma) [n*(4*n^2+12*n+11)/6+1/4-(-1)^n/4: n in [0..60]]; // _Vincenzo Librandi_, May 12 2015

%Y Cf. A000330, A000447, A002623.

%K nonn,easy

%O 0,2

%A _Floor van Lamoen_, Nov 19 2005

%E Closed formula adapted to the offset by _Bruno Berselli_, May 12 2015