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A304829 a(n) = 4024*7^n/147 - 256/3 (n >= 2). 2
1256, 9304, 65640, 459992, 3220456, 22543704, 157806440, 1104645592, 7732519656, 54127638104, 378893467240, 2652254271192, 18565779898856, 129960459292504, 909723215048040, 6368062505336792, 44576437537358056, 312035062761506904, 2184245439330548840 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

a(n) is the second Zagreb index of the crystal structure cubic carbon CCC(n), defined in the Baig et al. and in the Gao et al. references.

The second Zagreb  index of a simple connected graph is the sum of the degree products d(i)d(j) over all edges ij of the graph.

For n>=2 the M-polynomial of the crystal structure cubic carbon CCC(n) is M(CCC(n); x,y) = 72*7^(n-2)*x^3*y^3 + 24*7^(n-2)*x^3*y^4 + (76*7^(n-2) - 16)*x^4*y^4/3.

LINKS

Colin Barker, Table of n, a(n) for n = 2..1000

A. Q. Baig, M. Imran, W. Khalid, and M. Naeem, Molecular description of carbon graphite and crystal cubic carbon structures, Canadian J. Chem., 95, 674-686, 2017.

E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.

W. Gao, M. K. Siddiqui, M. Naeem and N. A. Rehman, Topological characterization of carbon graphite and crystal cubic carbon structures, Molecules, 22, 1496, 1-12, 2017.

Index entries for linear recurrences with constant coefficients, signature (8,-7).

FORMULA

From Bruno Berselli, May 21 2018: (Start)

G.f.: 8*x^2*(157 - 93*x)/((1 - x)*(1 - 7*x)).

a(n) = 8*a(n-1) - 7*a(n-2) = 7*a(n-1) + 512.

a(n) = (8/3)*(503*7^(n-2) - 32). (End)

MAPLE

seq((4024*7^(n-2)-256)*(1/3), n = 2 .. 25);

MATHEMATICA

Table[4024 7^n/147 - 256/3, {n, 2, 30}] (* Bruno Berselli, May 21 2018 *)

LinearRecurrence[{8, -7}, {1256, 9304}, 30] (* Harvey P. Dale, Jan 16 2019 *)

PROG

(PARI) Vec( 8*x^2*(157 - 93*x)/((1 - x)*(1 - 7*x)) + O(x^40)) \\ Colin Barker, May 23 2018

CROSSREFS

Cf. A304826, A304827, A304828.

Sequence in context: A080718 A219993 A237562 * A216941 A159726 A048130

Adjacent sequences:  A304826 A304827 A304828 * A304830 A304831 A304832

KEYWORD

nonn,easy

AUTHOR

Emeric Deutsch, May 21 2018

STATUS

approved

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Last modified August 26 01:34 EDT 2019. Contains 326324 sequences. (Running on oeis4.)