A018839 Squares on infinite chessboard at n moves from center using a {2,3} fairy knight.

1, 8, 32, 88, 192, 304, 372, 416, 472, 540, 608, 676, 744, 812, 880, 948, 1016, 1084, 1152, 1220, 1288, 1356, 1424, 1492, 1560, 1628, 1696, 1764, 1832, 1900, 1968, 2036, 2104, 2172, 2240, 2308, 2376, 2444, 2512, 2580, 2648, 2716, 2784, 2852, 2920, 2988

Offset: 0

Author

Marc LeBrun

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A297740 (partial sums).

Programs

Mathematica

CoefficientList[Series[(x + 1) (12 x^8 - 24 x^6 - 20 x^5 + 28 x^4 + 20 x^3 + 12 x^2 + 5*x + 1)/(x - 1)^2, {x, 0, 50}], x] (* Vincenzo Librandi, Oct 16 2013 *)

Formula

For n >= 8, a(n) = 68n - 72. - David W. Wilson

G.f.: (x+1)*(12*x^8 - 24*x^6 - 20*x^5 + 28*x^4 + 20*x^3 + 12*x^2 + 5*x + 1)/(x-1)^2. - Colin Barker, Oct 04 2012