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%I #13 Dec 07 2016 11:08:31
%S 1,1,2,3,4,5,6,7,8,10,12,15,18,22,26,31,36,42,49,56,64,72,82,94,106,
%T 121,139,157,179,205,231,262,298,334,376,425,481,537,601,673,745,827,
%U 921,1027,1133,1254,1393,1550,1707,1886,2091,2322,2553,2815,3113,3447,3781,4157,4582,5063,5600
%N Hexagonal spiral constructed on the nodes of the triangular net in which each new term is the sum of its two largest neighbors in the structure.
%C To evaluate a(n) consider only the two largest neighbors of a(n) that are present in the spiral when a(n) should be a new term in the spiral.
%C For the same idea but for an right triangle see A278645; for a square spiral see A278180.
%C It appears that the same idea for an isosceles triangle and also for a square array gives A030237.
%e Illustration of initial terms as a spiral:
%e .
%e . 18 - 15 - 12
%e . / \
%e . 22 3 - 2 10
%e . / / \ \
%e . 26 4 1 - 1 8
%e . \ \ /
%e . 31 5 - 6 - 7
%e . \
%e . 36 - 42 - 49
%e .
%e a(16) = 36 because the sum of its two largest neighbors is 31 + 5 = 36.
%e a(17) = 42 because the sum of its two largest neighbors is 36 + 6 = 42.
%e a(18) = 49 because the sum of its two largest neighbors is 42 + 7 = 49.
%e a(19) = 56 because the sum of its two largest neighbors is 49 + 7 = 56.
%Y Cf. A030237, A274920, A274921, A278180, A278181, A278645.
%K nonn
%O 0,3
%A _Omar E. Pol_, Nov 24 2016
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