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Number of squares on infinite quarter chessboard at <=n knight moves from the corner.
4

%I #9 Jun 17 2017 02:52:17

%S 1,3,12,32,59,91,130,176,229,289,356,430,511,599,694,796,905,1021,

%T 1144,1274,1411,1555,1706,1864,2029,2201,2380,2566,2759,2959,3166,

%U 3380,3601,3829,4064,4306,4555,4811,5074,5344,5621,5905,6196,6494,6799,7111,7430

%N Number of squares on infinite quarter chessboard at <=n knight moves from the corner.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F a(n) = (1/2) * (7*n^2 + n + 2), for n>3.

%F G.f.: -(2*x^6-2*x^5-4*x^4+4*x^3+6*x^2+1) / (x-1)^3. - _Colin Barker_, Jul 15 2013

%e 3 squares are reachable after 1 move, from these you can reach 8 new squares more, so a(1)=3, a(2)=12.

%Y First differences are in A047883.

%Y See A018836 (unbounded), A098498 (halfplane), A098499 (diagonal halfplane), A098501 (octant).

%K nonn,easy

%O 0,2

%A _Ralf Stephan_, Sep 15 2004

%E More terms from _Colin Barker_, Jul 15 2013