A319019 - OEIS

%I #47 Mar 06 2019 08:10:09

%S 0,1,8,8,40,8,56,24,120,8,56,48,240,40,208,56,280,8,56,48,240,64,384,

%T 120,568,56,264,144,688,112,560,136,648,8,56,48,240,64,384,136,648,72,

%U 400,232,1128,200,1048,240,1216,48,216,160,768,200,1176,352,1664

%N First differences of A319018.

%C Number of cells added at n-th stage to the structure of A319018.

%C See A319018 for further illustrations.

%H M. F. Hasler, <a href="/A319019/b319019.txt">Table of n, a(n) for n = 0..16384</a> (first 2050 terms from Rémy Sigrist)

%H Nathan Epstein, <a href="https://giant.gfycat.com/OblongNextCalf.webm">Gfycat animation of sequence</a>.

%H M. F. Hasler, <a href="/A319019/a319019.html">Interactive illustration of A319018 and A319019</a>.

%H N. J. A. Sloane, <a href="/A319019/a319019.png">Hand-drawn sketch showing terms through about the eighth shell</a>, but using offset a(0)=1. Illustrates the octagonal "castle walls".

%F Apparently, a(2^k + 1) = 8 for any k >= 0.

%F a(n) = 8*A322050(n) for all n > 1, see there for more formulas. - _M. F. Hasler_, Dec 18 2018

%o (PARI) A319019_upto(N,S=[],K=[[t\5-2,t%5-2]|t<-digits(6888528048,25)])={ vector(N,n, #N=if(n>1, S=setunion(S,N); N=vecsort(concat([[Vecsmall(Vec(n)+k)|k<-K]|n<-N])); S=setunion(Set(vecextract(N, select(i->N[i-1]==N[i],[2..#N]))),S);setminus(Set(N),S),[[0,0]]))} \\ Increase stack size with allocatemem() for N > 86. - _M. F. Hasler_, Dec 27 2018

%o (PARI) A319019(n)=sum(i=2,n,A322050(i))*8+(n>0) \\ _M. F. Hasler_, Dec 28 2018

%Y Cf. A319018.

%Y For further analysis see A322048, A322049, A322050.

%K nonn

%O 0,3

%A _Rémy Sigrist_, Sep 09 2018