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A094768
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Square spiral of sums of selected preceding terms, starting at 1 (a spiral Fibonacci-like sequence).
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4
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1, 1, 2, 3, 6, 9, 16, 25, 42, 68, 110, 179, 291, 470, 763, 1236, 2005, 3241, 5252, 8502, 13770, 22272, 36058, 58355, 94455, 152878, 247333, 400279, 647722, 1048180, 1696193, 2744373, 4440857, 7185700, 11627320, 18814256, 30443581, 49257837
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OFFSET
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1,3
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COMMENTS
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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 or vertically 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 only four positions are considered adjacent, eight however in A094767.
Clockwise and counterclockwise construction of the spiral result in the same sequence.
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LINKS
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EXAMPLE
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Clockwise constructed spiral begins
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13770--22272--36058--58355--94455
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8502 16-----25-----42-----68
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5252 9 1------1 110
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3241 6------3------2 179
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2005---1236----763----470----291
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where
a(2) = a(1) = 1,
a(3) = a(2) + a(1) = 2,
a(4) = a(3) + a(2) = 3,
a(5) = a(4) + a(3) + a(1) = 6,
a(6) = a(5) + a(4) = 9,
a(7) = a(6) + a(5) + a(1) = 16.
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PROG
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(PARI) {m=5; h=2*m-1; A=matrix(h, h); print1(A[m, m]=1, ", "); pj=m; pk=m; T=[[1, 0], [0, -1], [ -1, 0], [0, 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, 4, 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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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