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%I #24 Jun 14 2019 00:35:04
%S 0,2,8,14,24,34,48,62,80,98,120,142,168,194,224,254,288,322,360,398,
%T 440,482,528,574,624,674,728,782,840,898,960,1022,1088,1154,1224,1294,
%U 1368,1442,1520,1598,1680,1762,1848,1934,2024,2114,2208,2302,2400,2498,2600
%N Largest even number strictly less than n^2.
%C Longest non-intersecting route from (0, 0) to (n - 1, n - 1) staying in an (n - 1) X (n - 1) box (shortest route is length 2n A005843).
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).
%F a(n) = 2*ceiling[n^2/2] - 2 = 2*A074148(n) = A085046(n) - 1.
%F From _Colin Barker_, Jul 29 2012: (Start)
%F a(n) = (-1 + (-1)^n + 4*n + 2*n^2)/2.
%F a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4).
%F G.f.: 2*x*(1 + 2*x - x^2)/((1-x)^3*(1+x)). (End)
%F a(n) = n^2 - 2 for even n; a(n) = n^2 - 1 for odd n. -_Dennis P. Walsh_, Apr 15 2016
%p seq(2*ceil(n^2/2)-2,n=1..50);
%t Flatten[Table[{(2n - 1)^2 - 1, 4n^2 - 2}, {n, 25}]] (* _Alonso del Arte_, Apr 15 2016 *)
%o (PARI) lista(nn) = for(n=0, nn, print1((-1+(-1)^n+4*n+2*n^2)/2, ", ")); \\ _Altug Alkan_, Apr 15 2016
%K easy,nonn
%O 1,2
%A _Henry Bottomley_, Jul 06 2006
%E Offset corrected by _N. J. A. Sloane_, Apr 15 2016
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