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A278619
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.
3
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, 121, 139, 157, 179, 205, 231, 262, 298, 334, 376, 425, 481, 537, 601, 673, 745, 827, 921, 1027, 1133, 1254, 1393, 1550, 1707, 1886, 2091, 2322, 2553, 2815, 3113, 3447, 3781, 4157, 4582, 5063, 5600
OFFSET
0,3
COMMENTS
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.
For the same idea but for an right triangle see A278645; for a square spiral see A278180.
It appears that the same idea for an isosceles triangle and also for a square array gives A030237.
EXAMPLE
Illustration of initial terms as a spiral:
.
. 18 - 15 - 12
. / \
. 22 3 - 2 10
. / / \ \
. 26 4 1 - 1 8
. \ \ /
. 31 5 - 6 - 7
. \
. 36 - 42 - 49
.
a(16) = 36 because the sum of its two largest neighbors is 31 + 5 = 36.
a(17) = 42 because the sum of its two largest neighbors is 36 + 6 = 42.
a(18) = 49 because the sum of its two largest neighbors is 42 + 7 = 49.
a(19) = 56 because the sum of its two largest neighbors is 49 + 7 = 56.
CROSSREFS
KEYWORD
nonn
AUTHOR
Omar E. Pol, Nov 24 2016
STATUS
approved