A394197 Number of squares reachable in n (but no fewer) leaps of an antelope (the fairy chess piece) on an infinite chessboard.

1, 8, 32, 88, 192, 360, 608, 832, 960, 1040, 1112, 1212, 1332, 1456, 1580, 1704, 1828, 1952, 2076, 2200, 2324, 2448, 2572, 2696, 2820, 2944, 3068, 3192, 3316, 3440, 3564, 3688, 3812, 3936, 4060, 4184, 4308, 4432, 4556, 4680, 4804, 4928, 5052, 5176, 5300, 5424

Offset

0,2

Comments

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

Coordination sequence of the infinite antelope graph.

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

Eric Weisstein's World of Mathematics, Antelope Graph.

Wikipedia, Fairy chess piece.

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Formula

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

Mathematica

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

Crossrefs

Row 5 of A393393.

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

Sequence in context: A372981 A018839 A393839 * A008412 A014819 A033155

Adjacent sequences: A394194 A394195 A394196 * A394198 A394199 A394200

Keyword

nonn,easy

Author

Pontus von Brömssen, Mar 12 2026

Status

approved