A334741 Fill an infinite square array by following a spiral around the origin; in the central cell enter a(0)=1; thereafter, in the n-th cell, enter the sum of the entries of those earlier cells that are in the same row or column as that cell.

1, 1, 1, 2, 3, 5, 8, 11, 21, 40, 47, 93, 180, 203, 397, 796, 1576, 1675, 3305, 6636, 13192, 14004, 27607, 55029, 110192, 220024, 226740, 450123, 898661, 1798700, 3594248, 3704800, 7354303, 14681369, 29349536, 58710640, 117394896, 119196748, 237492079

Offset

0,4

Comments

The spiral track being used here is the same as in A274640, except that the starting cell here is indexed 0 (as in A274641).

The central cell gets index 0 (and we fill it in with the value a(0)=1).

Links

Peter Kagey, Table of n, a(n) for n = 0..2499

Example

Spiral begins:
     3----2----1
     |         |
     5    1----1   47
     |              |
     8---11---21---40
a(11) = 47 = 1 + 1 + 5 + 40, the sum of the cells in its row and column.

Prog

(PARI) \\ here P(n) returns A174344 and A274923 as pair.
P(n)={my(m=sqrtint(n), k=ceil(m/2)); n -= 4*k^2; if(n<0, if(n<-m, [k, 3*k+n], [-k-n, k]), if(n<m, [-k, k-n], [n-3*k, -k]))}
seq(n)={my(m=sqrtint(n)+1, k=ceil(m/2), sx=vector(m), sy=vector(m), v=vector(1+n)); v[1]=sx[k]=sy[k]=1; for(i=1, n, my([px, py]=P(i)); px+=k; py+=k; my(t=sx[px]+sy[py]); sx[px]+=t; sy[py]+=t; v[i+1]=t); v} \\ Andrew Howroyd, May 09 2020

Crossrefs

Cf. A280027.

Cf. A180714, A214526, A274640, A278180, A304586, A307834, A334742.

x- and y-coordinates are given by A174344 and A274923, respectively.

Sequence in context: A346116 A262841 A332070 * A259973 A092362 A105766

Adjacent sequences: A334738 A334739 A334740 * A334742 A334743 A334744

Keyword

nonn

Author

Alec Jones and Peter Kagey, May 09 2020

Status

approved