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 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. 2
 0, 5, 17, 42, 82, 143, 227, 340, 484, 665, 885, 1150, 1462, 1827, 2247, 2728, 3272, 3885, 4569, 5330, 6170, 7095, 8107, 9212, 10412, 11713, 13117, 14630, 16254, 17995, 19855, 21840, 23952, 26197, 28577, 31098, 33762, 36575, 39539, 42660, 45940 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS FORMULA a(n) = n*(4*n^2 + 12*n + 11)/6 + 1/4 - (-1)^n/4 = floor(A000447(n+1)/2). a(n) = 4*A002623(n-1) + A000330(n), with A002623(-1)=0. - Luce ETIENNE, May 12 2015 G.f.: x*(5 + 2*x + x^2)/((1-x)^4*(1+x)). - Vincenzo Librandi, May 12 2015 MAPLE seq(n*(4*n^2-1)/6 - 1/4 + 1/4*(-1)^n, n=1..50); MATHEMATICA Table[n (4 n^2 + 12 n + 11)/6 + 1/4 - (-1)^n/4, {n, 0, 60}] (* Vincenzo Librandi, May 12 2015 *) PROG (MAGMA) [n*(4*n^2+12*n+11)/6+1/4-(-1)^n/4: n in [0..60]]; // Vincenzo Librandi, May 12 2015 CROSSREFS Cf. A000330, A000447, A002623. Sequence in context: A052350 A318826 A239195 * A088645 A055609 A231703 Adjacent sequences:  A111743 A111744 A111745 * A111747 A111748 A111749 KEYWORD nonn,easy AUTHOR Floor van Lamoen, Nov 19 2005 EXTENSIONS Closed formula adapted to the offset by Bruno Berselli, May 12 2015 STATUS approved

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Last modified December 3 05:05 EST 2021. Contains 349445 sequences. (Running on oeis4.)