

A164001


Spiral of triangles around a hexagon.


16



1, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37, 49, 65, 86, 114, 151, 200, 265, 351, 465, 616, 816, 1081, 1432, 1897, 2513, 3329, 4410, 5842, 7739, 10252, 13581, 17991, 23833, 31572, 41824, 55405, 73396, 97229, 128801, 170625, 226030, 299426
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OFFSET

1,2


COMMENTS

a(n) is the side length of the nth triangle in a spiral around a hexagon with side length = 1.
Sequence very similar to A134816, but without repeated terms. Records in A134816. Also records in A000931, the Padovan sequence.
Column k=2 of A242464 (with offset 0).  Alois P. Heinz, May 19 2014


LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000
I. Amburg, K. Dasaratha, L. Flapan, T. Garrity, C. Lee, C. Mihailak, N. NeumannChun, S. Peluse, M. Stoffregen, Stern Sequences for a Family of Multidimensional Continued Fractions: TRIPStern Sequences, arXiv:1509.05239v1 [math.CO] 17 Sep 2015. See Conjecture 5.8.
Index entries for linear recurrences with constant coefficients, signature (0, 1, 1).


FORMULA

If n<5 then a(n) = n otherwise a(n) = a(n2)+a(n3).
G.f.: x1+(x^22*x1)/(1+x^2+x^3). a(n) = A000931(n+4) + A000931(n+5) = A000931(n+7), n>1.  R. J. Mathar, Oct 29 2009


MATHEMATICA

LinearRecurrence[{0, 1, 1}, {1, 2, 3, 4}, 50] (* Harvey P. Dale, Jul 08 2017 *)


CROSSREFS

The following are basically all variants of the same sequence: A000931, A078027, A096231, A124745, A133034, A134816, A164001, A182097, A228361 and probably A020720. However, each one has its own special features and deserves its own entry.
Sequence in context: A189083 A318156 A272948 * A117598 A120149 A117597
Adjacent sequences: A163998 A163999 A164000 * A164002 A164003 A164004


KEYWORD

easy,nonn


AUTHOR

Omar E. Pol, Oct 27 2009


STATUS

approved



