A319019 First differences of A319018.

0, 1, 8, 8, 40, 8, 56, 24, 120, 8, 56, 48, 240, 40, 208, 56, 280, 8, 56, 48, 240, 64, 384, 120, 568, 56, 264, 144, 688, 112, 560, 136, 648, 8, 56, 48, 240, 64, 384, 136, 648, 72, 400, 232, 1128, 200, 1048, 240, 1216, 48, 216, 160, 768, 200, 1176, 352, 1664

Offset: 0

Author

Rémy Sigrist, Sep 09 2018

Keywords

• nonn

Comments

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

See A319018 for further illustrations.

Links

• M. F. Hasler, Table of n, a(n) for n = 0..16384 (first 2050 terms from Rémy Sigrist)
• Nathan Epstein, Gfycat animation of sequence.
• M. F. Hasler, Interactive illustration of A319018 and A319019.
• N. J. A. Sloane, Hand-drawn sketch showing terms through about the eighth shell, but using offset a(0)=1. Illustrates the octagonal "castle walls".

Crossrefs

Cf. A319018.

For further analysis see A322048, A322049, A322050.

Programs

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

PARI

A319019(n)=sum(i=2,n,A322050(i))*8+(n>0) \\ M. F. Hasler, Dec 28 2018

Formula

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

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