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

0,3

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.

Links

Table of n, a(n) for n=0..60.

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

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

Sequence in context: A029750 A266480 A246080 * A173925 A320319 A263363

Adjacent sequences: A278616 A278617 A278618 * A278620 A278621 A278622

Keyword

nonn

Author

Omar E. Pol, Nov 24 2016

Status

approved