Search: id:A094768
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%I A094768
%S A094768 1,1,2,3,6,9,16,25,42,68,110,179,291,470,763,1236,2005,3241,5252,8502,
%T A094768 13770,22272,36058,58355,94455,152878,247333,400279,647722,1048180,
%U A094768 1696193,2744373,4440857,7185700,11627320,18814256,30443581,49257837
%N A094768 Square spiral of sums of selected preceding terms, starting at 1 (a spiral 
               Fibonacci-like sequence).
%C A094768 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.
%C A094768 a(1) = 1, a(n) = a(n-1) + Sum_{i < n-1 and a(i) is adjacent to a(n-1)} 
               a(i).
%C A094768 Here only four positions are considered adjacent, eight however in A094767.
%C A094768 Clockwise and counterclockwise construction of the spiral result in the 
               same sequence.
%H A094768 Klaus Brockhaus, <a href="b094768.txt">Table of n, a(n) for n=1..729</
               a>
%e A094768 Clockwise constructed spiral begins
%e A094768 13770..22272..36058..58355..94455
%e A094768 .8502.....16.....25.....42.....68
%e A094768 .5252......9......1......1....110
%e A094768 .3241......6......3......2....179
%e A094768 .2005...1236....763....470....291
%e A094768 where
%e A094768 a(2) = a(1) = 1,
%e A094768 a(3) = a(2)+a(1) = 2,
%e A094768 a(4) = a(3)+a(2) = 3,
%e A094768 a(5) = a(4)+a(3)+a(1) = 6,
%e A094768 a(6) = a(5)+a(4) = 9,
%e A094768 a(7) = a(6)+a(5)+a(1) = 16.
%o A094768 (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]
%Y A094768 Cf. A063826, A094767, A094769, A126937, A141481.
%Y A094768 Sequence in context: A007865 A052812 A062114 this_sequence A093830 A118033 
               A048810
%Y A094768 Adjacent sequences: A094765 A094766 A094767 this_sequence A094769 A094770 
               A094771
%K A094768 nonn
%O A094768 1,3
%A A094768 Yasutoshi Kohmoto (zbi74583(AT)boat.zero.ad.jp), Jun 10 2004
%E A094768 Edited and extended beyond a(14) by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), 
               Aug 27 2008

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