cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A111746 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.

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%I A111746 #12 Sep 08 2022 08:45:21
%S A111746 0,5,17,42,82,143,227,340,484,665,885,1150,1462,1827,2247,2728,3272,
%T A111746 3885,4569,5330,6170,7095,8107,9212,10412,11713,13117,14630,16254,
%U A111746 17995,19855,21840,23952,26197,28577,31098,33762,36575,39539,42660,45940
%N A111746 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 A111746 a(n) = n*(4*n^2 + 12*n + 11)/6 + 1/4 - (-1)^n/4 = floor(A000447(n+1)/2).
%F A111746 a(n) = 4*A002623(n-1) + A000330(n), with A002623(-1)=0. - _Luce ETIENNE_, May 12 2015
%F A111746 G.f.: x*(5 + 2*x + x^2)/((1-x)^4*(1+x)). - _Vincenzo Librandi_, May 12 2015
%p A111746 seq(n*(4*n^2-1)/6 - 1/4 + 1/4*(-1)^n,n=1..50);
%t A111746 Table[n (4 n^2 + 12 n + 11)/6 + 1/4 - (-1)^n/4, {n, 0, 60}] (* _Vincenzo Librandi_, May 12 2015 *)
%o A111746 (Magma) [n*(4*n^2+12*n+11)/6+1/4-(-1)^n/4: n in [0..60]]; // _Vincenzo Librandi_, May 12 2015
%Y A111746 Cf. A000330, A000447, A002623.
%K A111746 nonn,easy
%O A111746 0,2
%A A111746 _Floor van Lamoen_, Nov 19 2005
%E A111746 Closed formula adapted to the offset by _Bruno Berselli_, May 12 2015