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A094767 Square spiral of sums of selected preceding terms, starting at 1 (a spiral Fibonacci-like sequence). 4
1, 1, 2, 4, 8, 13, 26, 40, 81, 123, 205, 412, 620, 1034, 2072, 3120, 5204, 8332, 16677, 25056, 41772, 66854, 133748, 200749, 334741, 535694, 870558, 1741321, 2612619, 4355177, 6968828, 11324625, 22650284, 33978635, 56635145, 90624176, 147267645 (list; graph; refs; listen; history; text; internal format)
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

      |

      |

      |

  25056      26------40------81-----123

      |       |                       |

      |       |                       |

      |       |                       |

  16677      13       1-------1     205

      |       |               |       |

      |       |               |       |

      |       |               |       |

   8332       8-------4-------2     412

      |                               |

      |                               |

      |                               |

   5204----3120----2072----1034-----620

.

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

Cf. A063826, A094768, A094769, A126937, A141481.

Sequence in context: A043807 A043816 A048328 * A263292 A026643 A288925

Adjacent sequences:  A094764 A094765 A094766 * A094768 A094769 A094770

KEYWORD

nonn

AUTHOR

Yasutoshi Kohmoto, Jun 10 2004

EXTENSIONS

Edited and extended beyond a(14) by Klaus Brockhaus, Aug 27 2008

STATUS

approved

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Last modified August 4 07:32 EDT 2020. Contains 336201 sequences. (Running on oeis4.)