A322056 - OEIS

%I #16 Dec 22 2018 03:45:11

%S 1,8,32,32,72,40,136,64,192,72,232,112,304,104,328,160,416,136,424,

%T 208,528,168,520,256,640,200,616,304,752,232,712,352,864,264,808,400,

%U 976,296,904,448,1088,328,1000,496,1200,360,1096,544,1312,392,1192,592,1424

%N First differences of A322055.

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

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

%H Rémy Sigrist, <a href="/A322056/b322056.txt">Table of n, a(n) for n = 0..1000</a>

%H N. J. A. Sloane, <a href="/A322055/a322055.png">Illustration of a(0) to a(5).</a>

%F Conjectures from _Colin Barker_, Dec 22 2018: (Start)

%F 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).

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

%F (End)

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

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Dec 21 2018

%E More terms from _Rémy Sigrist_, Dec 22 2018