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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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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 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
| Klaus Brockhaus, Table of n, a(n) for n=1..729
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EXAMPLE
| Clockwise constructed spiral begins
13770..22272..36058..58355..94455
.8502.....16.....25.....42.....68
.5252......9......1......1....110
.3241......6......3......2....179
.2005...1236....763....470....291
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
| (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)} [From Klaus Brockhaus, Aug 27 2008]
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CROSSREFS
| Cf. A063826, A094767, A094769, A126937, A141481.
Sequence in context: A007865 A052812 A062114 * A093830 A118033 A048810
Adjacent sequences: A094765 A094766 A094767 * A094769 A094770 A094771
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KEYWORD
| nonn
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AUTHOR
| Yasutoshi Kohmoto (zbi74583(AT)boat.zero.ad.jp), Jun 10 2004
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EXTENSIONS
| Edited and extended beyond a(14) by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Aug 27 2008
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