login
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
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
B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral clusters, Inorgan. Chem. 24 (1985), 4545-4558.
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(n-1) - 3*a(n-2) + a(n-3) 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
KEYWORD
nonn,easy
AUTHOR
Brian Watson, Jan 13 2018
EXTENSIONS
Entry revised by N. J. A. Sloane, Jan 22 2018
STATUS
approved