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

0,3

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".

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

Prog

(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

Crossrefs

Cf. A319018.

For further analysis see A322048, A322049, A322050.

Sequence in context: A339340 A341247 A188275 * A278846 A339323 A240037

Adjacent sequences: A319016 A319017 A319018 * A319020 A319021 A319022

Keyword

nonn

Author

Rémy Sigrist, Sep 09 2018

Status

approved