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), 4545-4558.
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(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
KEYWORD
nonn,easy
AUTHOR
Brian Watson, Jan 13 2018
EXTENSIONS
Entry revised by N. J. A. Sloane, Jan 22 2018
STATUS
approved