1,4

Enter 0 into center position and 1 into next position of the spiral. Repeat: Add to the number in the present position the numbers in all those already filled positions that are horizontally, vertically or diagonally adjacent to it, go to next position of the spiral and enter the sum into it.

a(1) = 0, a(2) = 1, a(n) = a(n-1) + Sum_{i < n-1 and a(i) is adjacent to a(n-1)} a(i).

As in A094767 eight positions are considered adjacent here.

Clockwise and counterclockwise construction of the spiral result in the same sequence.

Klaus Brockhaus, Table of n, a(n) for n=1..729

Clockwise constructed spiral begins

19202..30732..61482..92281.153874

11518.....12.....18.....37.....56

.7666..... 6......0......1.....94

.3830......4......2......1....189

.2392...1434....952....475....285

where

a(1) = 0,

a(2) = 1,

a(3) = a(2)+a(1) = 1,

a(4) = a(3)+a(2)+a(1) = 2,

a(5) = a(4)+a(3)+a(2)+a(1) = 4,

a(6) = a(5)+a(4)+a(1) = 6,

a(7) = a(6)+a(5)+a(4)+a(1) = 12.

(PARI) {m=5; h=2*m-1; A=matrix(h, h); print1(A[m, m]=0, ", "); print1(A[m, m+1]=1, ", "); pj=m; pk=m+1; T=[[1, 0], [1, -1], [0, -1], [ -1, -1], [ -1, 0], [ -1, 1], [0, 1], [1, 1]]; for(n=2, (h-2)^2-1, g=sqrtint(n); r=(g+g%2)\2; q=4*r^2; d=n-q; if(n<=q-2*r, j=d+3*r; k=r, if(n<=q, j=r; k=-d-r, if(n<=q+2*r, j=r-d; k=-r, j=-r; k=d-3*r))); j=j+m; k=k+m; s=A[pj, pk]; for(c=1, 8, v=[pj, pk]; v+=T[c]; s=s+A[v[1], v[2]]); A[j, k]=s; print1(s, ", "); pj=j; pk=k)} [From Klaus Brockhaus, Aug 27 2008]

Cf. A063826, A094767, A094768, A126937, A141481.

Sequence in context: A104352 A133488 A068911 this_sequence A068018 A060798 A134320

Adjacent sequences: A094766 A094767 A094768 this_sequence A094770 A094771 A094772

nonn

Yasutoshi Kohmoto (zbi74583(AT)boat.zero.ad.jp), Jun 10 2004

Edited and extended beyond a(12) by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Aug 27 2008