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

0,3

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.

Links

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

Example

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.

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 *)

Crossrefs

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

Sequence in context: A211656 A051204 A335154 * A232566 A192649 A102363

Adjacent sequences: A278178 A278179 A278180 * A278182 A278183 A278184

Keyword

nonn

Author

Omar E. Pol, Nov 14 2016

Status

approved