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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. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A254351 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

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Last modified June 21 04:10 EDT 2021. Contains 345354 sequences. (Running on oeis4.)