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A094768 Square spiral of sums of selected preceding terms, starting at 1 (a spiral Fibonacci-like sequence). 4
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; 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 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.

LINKS

Klaus Brockhaus, Table of n, a(n) for n = 1..729

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.

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)} \\ Klaus Brockhaus, Aug 27 2008

CROSSREFS

Cf. A063826, A094767, A094769, A126937, A141481.

Sequence in context: A218153 A319642 A062114 * A301753 A275548 A260710

Adjacent sequences:  A094765 A094766 A094767 * A094769 A094770 A094771

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 September 18 03:39 EDT 2020. Contains 337164 sequences. (Running on oeis4.)