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

Author

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

Keywords

• nonn

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.

Examples

			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
		

Links

• Klaus Brockhaus, Table of n, a(n) for n=1..961
• Eric Wastl, Day 3 Spiral Memory Part Two, Advent of Code 2017.

Crossrefs

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

Programs

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

Extensions

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