

A334742


Pascal's spiral: starting with a(1) = 1, proceed in a square spiral, computing each term as the sum of horizontally and vertically adjacent prior terms.


7



1, 1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 7, 7, 8, 10, 12, 12, 14, 17, 20, 20, 23, 27, 32, 37, 37, 42, 48, 55, 62, 62, 69, 77, 87, 99, 111, 111, 123, 137, 154, 174, 194, 194, 214, 237, 264, 296, 333, 370, 370, 407, 449, 497, 552, 614, 676, 676, 738, 807, 884, 971, 1070
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OFFSET

1,4


COMMENTS

This is the square spiral analogy of Pascal's triangle thought of as a table read by antidiagonals.


LINKS

Peter Kagey, Table of n, a(n) for n = 1..10000
Peter Kagey, Bitmap illustrating the of parity of the first 2^20=1048576 terms. (Even and odd numbers are represented with black and white pixels respectively.)


FORMULA

a(A033638(n)) = a(A002620(n)) for n > 1.


EXAMPLE

Spiral begins:
1119987776962

12121087 62
  
14 221 7 55
    
17 3 11 6 48
   
20 3455 42
 
202327323737
a(15) = 10 = 8 + 2, the sum of the cells immediately to the right and below. The term to the left is not included in the sum because it has not yet occurred in the spiral.


CROSSREFS

Cf. A007318, A141481, A334688.
Cf. A180714, A214526, A274640, A278180, A304586, A307834, A334741.
x and ycoordinates are given by A174344 and A274923, respectively.
Sequence in context: A024699 A083479 A112231 * A213856 A173329 A241951
Adjacent sequences: A334739 A334740 A334741 * A334743 A334744 A334745


KEYWORD

nonn,nice


AUTHOR

Alec Jones and Peter Kagey, May 09 2020


STATUS

approved



