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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.

%I A334742 #30 Apr 12 2023 10:52:25
%S A334742 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 A334742 48,55,62,62,69,77,87,99,111,111,123,137,154,174,194,194,214,237,264,
%U A334742 296,333,370,370,407,449,497,552,614,676,676,738,807,884,971,1070
%N 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.
%C A334742 This is the square spiral analogy of Pascal's triangle thought of as a table read by antidiagonals.
%H A334742 Peter Kagey, <a href="/A334742/b334742.txt">Table of n, a(n) for n = 1..10000</a>
%H A334742 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 A334742 a(A033638(n)) = a(A002620(n)) for n > 1.
%e A334742 Spiral begins:
%e A334742   111--99--87--77--69--62
%e A334742                         |
%e A334742    12--12--10---8---7  62
%e A334742     |               |   |
%e A334742    14   2---2---1   7  55
%e A334742     |   |       |   |   |
%e A334742    17   3   1---1   6  48
%e A334742     |   |           |   |
%e A334742    20   3---4---5---5  42
%e A334742     |                   |
%e A334742    20--23--27--32--37--37
%e A334742 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 A334742 Cf. A007318, A141481, A334688.
%Y A334742 Cf. A180714, A214526, A274640, A278180, A304586, A307834, A334741.
%Y A334742 x- and y-coordinates are given by A174344 and A274923, respectively.
%K A334742 nonn,nice
%O A334742 1,4
%A A334742 _Alec Jones_ and _Peter Kagey_, May 09 2020