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Number of squares on infinite half chessboard at <=n knight moves from a fixed point on the diagonal.
4

%I #8 Jun 17 2017 04:00:45

%S 1,5,23,57,109,169,246,334,439,555,688,832,993,1165,1354,1554,1771,

%T 1999,2244,2500,2773,3057,3358,3670,3999,4339,4696,5064,5449,5845,

%U 6258,6682,7123,7575,8044,8524,9021,9529,10054,10590,11143,11707,12288,12880,13489

%N Number of squares on infinite half chessboard at <=n knight moves from a fixed point on 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) = (1/4) [28n^2 - 6n + 9 + 3(-1)^n], for n>3.

%F G.f.: -(3*x^7-x^6-8*x^5+4*x^4+13*x^3+13*x^2+3*x+1) / ((x-1)^3*(x+1)). - _Colin Barker_, Jul 14 2013

%e 5 squares are reachable after 1 move, from these you can reach 18 new squares more, so a(1)=5, a(2)=23.

%Y Equals A098498(n) - A052938(n-4), n>3.

%Y See A018836 (unbounded), A098498 (halfplane), A098500 (quadrant), A098501 (octant).

%K nonn,easy

%O 0,2

%A _Ralf Stephan_, Sep 15 2004

%E More terms from _Colin Barker_, Jul 14 2013