A278181 Hexagonal spiral constructed on the nodes of the triangular net in which each new term is the sum of its neighbors.

1, 1, 2, 3, 4, 5, 7, 8, 9, 12, 14, 19, 22, 29, 33, 42, 47, 59, 74, 82, 99, 108, 129, 155, 169, 202, 243, 265, 316, 378, 411, 486, 575, 622, 728, 861, 1017, 1099, 1280, 1487, 1595, 1832, 2116, 2440, 2609, 2980, 3425, 3933, 4198, 4779, 5473, 6262, 6673, 7570, 8631, 9828, 10450, 11800, 13389, 15267, 17383

Offset: 0

Author

Omar E. Pol, Nov 14 2016

Keywords

• nonn

Comments

To evaluate a(n) consider the neighbors of a(n) that are present in the spiral when a(n) should be a new term in the spiral.

Examples

			Illustration of initial terms as a spiral:
.
.             22 - 19 - 14
.             /          \
.           29    3 - 2   12
.           /    /     \   \
.         33    4   1 - 1   9
.           \    \         /
.           42    5 - 7 - 8
.             \
.             47 - 59 - 74
.
a(16) = 47 because the sum of its two neighbors is 42 + 5 = 47.
a(17) = 59 because the sum of its three neighbors is 47 + 5 + 7 = 59.
a(18) = 74 because the sum of its three neighbors is 59 + 7 + 8 = 74.
a(19) = 82 because the sum of its two neighbors is 74 + 8 = 82.
		

Links

• JungHwan Min, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A047931, A064642, A122479, A141481, A274821, A274921, A275606, A275610.

Programs

Mathematica

A278181[0] = A278181[1] = 1; A278181[n_] := A278181[n] = With[{lev = Ceiling[1/6 (-3 + Sqrt[3] Sqrt[3 + 4 n])]}, With[{pos = 3 lev (lev - 1) + (n - 3 lev (1 + lev))/lev*(lev - 1)}, A278181[n - 1] + A278181[Ceiling[pos]] + If[Mod[n, lev] == 0 || n - 3 lev (lev - 1) == 1, 0, A278181[Floor[pos]]] + If[3 lev (1 + lev) == n, A278181[n - 6 lev + 1], 0]]]; Array[A278181, 61, 0] (* JungHwan Min, Nov 21 2016 *)