A305270 a(n) = 140*2^n - 112.

28, 168, 448, 1008, 2128, 4368, 8848, 17808, 35728, 71568, 143248, 286608, 573328, 1146768, 2293648, 4587408, 9174928, 18349968, 36700048, 73400208, 146800528, 293601168, 587202448, 1174405008, 2348810128, 4697620368, 9395240848, 18790481808, 37580963728, 75161927568, 150323855248

Offset: 0

Author

Emeric Deutsch, May 30 2018

Keywords

• nonn
• easy

Comments

a(n) is the number of edges in the polyphenylene dendrimer G[n], defined pictorially in the Arif et al. reference (see Fig. 1, where G[2] is shown).

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• N. E. Arif, Roslan Hasni and Saeid Alikhani, Fourth order and fourth sum connectivity indices of polyphenylene dendrimers, J. Applied Science, 12 (21), 2012, 2279-2282.
• Index entries for linear recurrences with constant coefficients, signature (3,-2).

Crossrefs

Cf. A305269, A305271, A305272.

Programs

Maple

seq(140*2^n-112, n = 0..40);

PARI

Vec(28*(1 + 3*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 31 2018

Formula

From Colin Barker, May 31 2018: (Start)

G.f.: 28*(1 + 3*x) / ((1 - x)*(1 - 2*x)).

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

(End)