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.

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

Author

Omar E. Pol, Nov 24 2016

Keywords

• nonn

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.

Examples

			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

Cf. A030237, A274920, A274921, A278180, A278181, A278645.