OFFSET
1,3
COMMENTS
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.
LINKS
Klaus Brockhaus, Table of n, a(n) for n = 1..729
EXAMPLE
Clockwise constructed spiral begins
.
41772---66854--133748--200749--334741
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25056 26------40------81-----123
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16677 13 1-------1 205
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8332 8-------4-------2 412
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5204----3120----2072----1034-----620
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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.
PROG
(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)} \\ Klaus Brockhaus, Aug 27 2008
CROSSREFS
KEYWORD
nonn
AUTHOR
Yasutoshi Kohmoto, Jun 10 2004
EXTENSIONS
Edited and extended beyond a(14) by Klaus Brockhaus, Aug 27 2008
STATUS
approved