1,3

Enter 1 into center 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) = 1, a(n) = a(n-1) + Sum_{i < n-1 and a(i) is adjacent to a(n-1)} a(i).

Here eight positions are considered adjacent, only four however in A094768.

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

41772..66854.133748.200749.334741

25056.....26.....40.....81....123

16677.....13......1......1....205

.8332......8......4......2....412

.5204...3120...2072...1034....620

where

a(2) = a(1) = 1,

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

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

a(5) = a(4)+a(3)+a(2)+a(1) = 8,

a(6) = a(5)+a(4)+a(1) = 13,

a(7) = a(6)+a(5)+a(4)+a(1) = 26.

(PARI) {m=5; h=2*m-1; A=matrix(h, h); print1(A[m, m]=1, ", "); pj=m; pk=m; T=[[1, 0], [1, -1], [0, -1], [ -1, -1], [ -1, 0], [ -1, 1], [0, 1], [1, 1]]; for(n=1, (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, A094768, A094769, A126937, A141481.

Sequence in context: A043807 A043816 A048328 this_sequence A026643 A018285 A026665

Adjacent sequences: A094764 A094765 A094766 this_sequence A094768 A094769 A094770

nonn

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

Edited and extended beyond a(14) by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Aug 27 2008