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Search: id:A141481
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| A141481 |
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Square spiral of sums of selected preceding terms, starting at 1. |
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+0
4
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| 1, 1, 2, 4, 5, 10, 11, 23, 25, 26, 54, 57, 59, 122, 133, 142, 147, 304, 330, 351, 362, 747, 806, 880, 931, 957, 1968, 2105, 2275, 2391, 2450, 5022, 5336, 5733, 6155, 6444, 6591, 13486, 14267, 15252, 16295, 17008, 17370, 35487, 37402, 39835, 42452, 45220
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Enter 1 into center position of the spiral. Repeat: Go to next position of the spiral and enter into that position the sum of the numbers in those already filled positions that are horizontally, vertically or diagonally adjacent to it.
Clockwise and counterclockwise construction of the spiral result in the same sequence.
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LINKS
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K. Brockhaus, Table of n, a(n) for n=1..961
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EXAMPLE
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Clockwise constructed spiral begins
362..747..806..880..931
351...11...23...25...26
330...10....1....1...54
304....5....4....2...57
147..142..133..122...59
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PROGRAM
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(PARI) {m=5; h=2*m-1; A=matrix(h, h); print1(A[m, m]=1, ", "); 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=0; for(c=1, 8, v=[j, k]; v+=T[c]; s=s+A[v[1], v[2]]); A[j, k]=s; print1(s, ", "))} [From Klaus Brockhaus, Aug 27 2008]
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CROSSREFS
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Cf. A063826, A094767, A094768, A094769, A126937.
Sequence in context: A091856 A083416 A022770 this_sequence A047611 A120491 A022944
Adjacent sequences: A141478 A141479 A141480 this_sequence A141482 A141483 A141484
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KEYWORD
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nonn
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AUTHOR
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Niclas Rantala (nrantala(AT)hotmail.com), Aug 09 2008
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EXTENSIONS
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Edited and extended beyond a(9) by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Aug 27 2008
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