A298125 The hex numbers (A003215) together with 3.

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

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

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