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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 5 13:14 EDT 2020. Contains 333241 sequences. (Running on oeis4.)