A141481 Square spiral of sums of selected preceding terms, starting at 1.

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

Offset

1,3

Comments

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.

Links

Klaus Brockhaus, Table of n, a(n) for n=1..961

Eric Wastl, Day 3 Spiral Memory Part Two, Advent of Code 2017.

Example

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

Prog

(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, ", "))} \\ Klaus Brockhaus, Aug 27 2008

Crossrefs

Cf. A063826, A094767, A094768, A094769, A126937.

Sequence in context: A091856 A083416 A022770 * A241268 A285697 A047611

Adjacent sequences: A141478 A141479 A141480 * A141482 A141483 A141484

Keyword

nonn

Author

Niclas Rantala (nrantala(AT)hotmail.com), Aug 09 2008

Extensions

Edited and extended beyond a(9) by Klaus Brockhaus, Aug 27 2008

Status

approved