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%I #30 Apr 12 2023 10:52:25
%S 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,
%T 48,55,62,62,69,77,87,99,111,111,123,137,154,174,194,194,214,237,264,
%U 296,333,370,370,407,449,497,552,614,676,676,738,807,884,971,1070
%N 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.
%C This is the square spiral analogy of Pascal's triangle thought of as a table read by antidiagonals.
%H Peter Kagey, <a href="/A334742/b334742.txt">Table of n, a(n) for n = 1..10000</a>
%H Peter Kagey, <a href="/A334742/a334742.png">Bitmap illustrating the parity of the first 2^20=1048576 terms</a>. (Even and odd numbers are represented with black and white pixels respectively.)
%F a(A033638(n)) = a(A002620(n)) for n > 1.
%e Spiral begins:
%e 111--99--87--77--69--62
%e |
%e 12--12--10---8---7 62
%e | | |
%e 14 2---2---1 7 55
%e | | | | |
%e 17 3 1---1 6 48
%e | | | |
%e 20 3---4---5---5 42
%e | |
%e 20--23--27--32--37--37
%e 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.
%Y Cf. A007318, A141481, A334688.
%Y Cf. A180714, A214526, A274640, A278180, A304586, A307834, A334741.
%Y x- and y-coordinates are given by A174344 and A274923, respectively.
%K nonn,nice
%O 1,4
%A _Alec Jones_ and _Peter Kagey_, May 09 2020
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