A304836 a(n) = 27*n^2 - 51*n + 24, n>=1.

0, 30, 114, 252, 444, 690, 990, 1344, 1752, 2214, 2730, 3300, 3924, 4602, 5334, 6120, 6960, 7854, 8802, 9804, 10860, 11970, 13134, 14352, 15624, 16950, 18330, 19764, 21252, 22794, 24390, 26040, 27744, 29502, 31314, 33180, 35100, 37074, 39102, 41184, 43320, 45510, 47754, 50052, 52404

Offset: 1

Author

Emeric Deutsch, May 21 2018

Keywords

• nonn
• easy

Comments

a(n) is the number of edges in the hex derived network HDN1(n) from the Manuel et al. reference (see HDN1(4) in Fig. 8).

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• P. Manuel, R. Bharati, I. Rajasingh, and Chris Monica M, On minimum metric dimension of honeycomb networks, J. Discrete Algorithms, 6, 2008, 20-27.
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A082040, A304837, A304838.

Programs

GAP

List([1..50], n->27*n^2-51*n+24); # Muniru A Asiru, May 21 2018

Maple

seq(27*n^2-51*n+24, n = 1 .. 45);

PARI

concat(0, Vec(6*x^2*(5 + 4*x) / (1 - x)^3 + O(x^40))) \\ Colin Barker, May 23 2018

Formula

From Colin Barker, May 23 2018: (Start)

G.f.: 6*x^2*(5 + 4*x) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3.

(End)