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
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).
Crossrefs
Cf. A003215.
Programs
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PARI
Vec(x*(1 + x^2 + 6*x^3 - 2*x^4) / (1 - x)^3 + O(x^60)) \\ Colin Barker, Feb 05 2018
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)
Extensions
Entry revised by N. J. A. Sloane, Jan 22 2018
Comments