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%I #8 Jun 17 2017 04:00:45
%S 1,2,5,13,31,49,70,93,121,151,186,223,265,309,358,409,465,523,586,651,
%T 721,793,870,949,1033,1119,1210,1303,1401,1501,1606,1713,1825,1939,
%U 2058,2179,2305,2433,2566,2701,2841,2983,3130,3279,3433,3589,3750,3913,4081
%N Number of squares on infinite octant of chessboard at <=n knight moves from the corner. The octant includes the diagonal.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).
%F a(n) = (1/8) * [14n^2 + 8n + 5 + 3(-1)^n], for n>4.
%F G.f.: -(2*x^8+2*x^7-7*x^6-5*x^5+8*x^4+5*x^3+x^2+1) / ((x-1)^3*(x+1)). - _Colin Barker_, Jul 14 2013
%e 2 squares are reachable after 1 move, from these you can reach 3 new squares more, so a(1)=2, a(2)=5.
%Y See A018836 (unbounded), A098498 (halfplane), A098499 (diagonal halfplane), A098500 (quadrant).
%K nonn,easy
%O 0,2
%A _Ralf Stephan_, Sep 15 2004
%E More terms from _Colin Barker_, Jul 14 2013
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