

A298125


The hex numbers (A003215) together with 3.


1



1, 3, 7, 19, 37, 61, 91, 127, 169, 217, 271, 331, 397, 469, 547, 631, 721, 817, 919, 1027, 1141, 1261, 1387, 1519, 1657, 1801, 1951, 2107, 2269, 2437, 2611, 2791, 2977, 3169, 3367, 3571, 3781, 3997, 4219, 4447, 4681, 4921, 5167, 5419, 5677, 5941, 6211, 6487
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OFFSET

1,2


COMMENTS

Apart from the term 3, these are precisely the sizes of hexagonal clusters of circles in the A_2 (or hexagonal) lattice.
These numbers include many common numbers of strands used in cables.


LINKS

Colin Barker, Table of n, a(n) for n = 1..1000
B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral clusters, Inorgan. Chem. 24 (1985), 45454558.
Wikipedia, Wire: Number of strands
Index entries for linear recurrences with constant coefficients, signature (3,3,1).


FORMULA

From Colin Barker, Feb 05 2018: (Start)
G.f.: x*(1 + x^2 + 6*x^3  2*x^4) / (1  x)^3.
a(n) = 7  9*n + 3*n^2 for n>2.
a(n) = 3*a(n1)  3*a(n2) + a(n3) for n>5.
(End)


PROG

(PARI) Vec(x*(1 + x^2 + 6*x^3  2*x^4) / (1  x)^3 + O(x^60)) \\ Colin Barker, Feb 05 2018


CROSSREFS

Cf. A003215.
Sequence in context: A049490 A112391 A127928 * A047025 A222465 A239416
Adjacent sequences: A298122 A298123 A298124 * A298126 A298127 A298128


KEYWORD

nonn,easy


AUTHOR

Brian Watson, Jan 13 2018


EXTENSIONS

Entry revised by N. J. A. Sloane, Jan 22 2018


STATUS

approved



