

A334741


Fill an infinite square array by following a spiral around the origin; in the central cell enter a(0)=1; thereafter, in the nth 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
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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:
321
 
5 11 47
 
8112140
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], [kn, k]), if(n<m, [k, kn], [n3*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 ycoordinates 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



