A322056 First differences of A322055.

1, 8, 32, 32, 72, 40, 136, 64, 192, 72, 232, 112, 304, 104, 328, 160, 416, 136, 424, 208, 528, 168, 520, 256, 640, 200, 616, 304, 752, 232, 712, 352, 864, 264, 808, 400, 976, 296, 904, 448, 1088, 328, 1000, 496, 1200, 360, 1096, 544, 1312, 392, 1192, 592, 1424

Offset: 0

Author

N. J. A. Sloane, Dec 21 2018

Keywords

• nonn

Comments

Number of cells turned ON at generation n of the knight's-move cellular automaton described in A322055.

This is another knight's-move version of the Ulam-Warburton cellular automaton (see A147562).

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..1000
• N. J. A. Sloane, Illustration of a(0) to a(5).

Crossrefs

Cf. A139250, A147562, A319018, A319019, A322055.

Formula

Conjectures from Colin Barker, Dec 22 2018: (Start)

G.f.: (1 + 8*x + 32*x^2 + 32*x^3 + 70*x^4 + 24*x^5 + 72*x^6 + 49*x^8 - 8*x^10 + 16*x^11 - 8*x^12) / ((1 - x)^2*(1 + x)^2*(1 + x^2)^2).

a(n) = 2*a(n-4) - a(n-8) for n>8.

(End)

Extensions

More terms from Rémy Sigrist, Dec 22 2018