A394197 - OEIS

%I #11 Mar 19 2026 17:10:47

%S 1,8,32,88,192,360,608,832,960,1040,1112,1212,1332,1456,1580,1704,

%T 1828,1952,2076,2200,2324,2448,2572,2696,2820,2944,3068,3192,3316,

%U 3440,3564,3688,3812,3936,4060,4184,4308,4432,4556,4680,4804,4928,5052,5176,5300,5424

%N Number of squares reachable in n (but no fewer) leaps of an antelope (the fairy chess piece) on an infinite chessboard.

%C An antelope is a (3,4)-leaper.

%C Coordination sequence of the infinite antelope graph.

%H Paolo Xausa, <a href="/A394197/b394197.txt">Table of n, a(n) for n = 0..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AntelopeGraph.html">Antelope Graph</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Fairy_chess_piece">Fairy chess piece</a>.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F a(n) = 124*n-156 for n >= 12.

%t LinearRecurrence[{2, -1}, {1, 8, 32, 88, 192, 360, 608, 832, 960, 1040, 1112, 1212, 1332, 1456}, 50] (* _Paolo Xausa_, Mar 15 2026 *)

%Y Row 5 of A393393.

%Y Cf. A018842 (knight), A018839 (zebra), A393839 (giraffe), A394194, A394195, A394196.

%K nonn,easy

%O 0,2

%A _Pontus von Brömssen_, Mar 12 2026