A098500 - OEIS

A098500

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

1, 3, 12, 32, 59, 91, 130, 176, 229, 289, 356, 430, 511, 599, 694, 796, 905, 1021, 1144, 1274, 1411, 1555, 1706, 1864, 2029, 2201, 2380, 2566, 2759, 2959, 3166, 3380, 3601, 3829, 4064, 4306, 4555, 4811, 5074, 5344, 5621, 5905, 6196, 6494, 6799, 7111, 7430

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..46.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

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

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

EXAMPLE

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

CROSSREFS