A277106 -id:A277106 - cp's OEIS frontend

0, 96, 384, 1248, 3840, 11616, 34944, 104928, 314880, 944736, 2834304, 8503008, 25509120, 76527456, 229582464, 688747488, 2066242560, 6198727776, 18596183424, 55788550368, 167365651200, 502096953696, 1506290861184, 4518872583648, 13556617751040

Offset: 1

Emeric Deutsch, Nov 05 2016

a(n) is the second Zagreb index of the Sierpiński [Sierpinski] gasket graph S[n] (n>=2).
The second Zagreb index of a simple connected graph g is the sum of the degree products d(i)d(j) over all edges ij of g.
The M-polynomial of the Sierpinski gasket graph S[n] is  M(S[n], x, y) = 6*x^2*y^4 + (3^n - 6)*x^4*y^4.

E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
Eric Weisstein's World of Mathematics, Sierpiński Gasket Graph.
Index entries for linear recurrences with constant coefficients, signature (4,-3).

Cf. A277106.

Maple
```
seq(16*3^n-48, n = 1..30);
```

Table[16*3^n - 48, {n, 25}] (* or *) Rest@ CoefficientList[Series[96 x^2/((1 - x) (1 - 3 x)), {x, 0, 25}], x] (* Michael De Vlieger, Nov 06 2016 *)
LinearRecurrence[{4,-3},{0,96},30] (* Harvey P. Dale, Dec 20 2024 *)

G.f.: 96*x^2/((1 - x)*(1 - 3*x)).
a(n) = 4*a(n-1) - 3*a(n-2).
a(n) = 96*A003462(n-1). - R. J. Mathar, Apr 07 2022

cp's OEIS Frontend

A277107 a(n) = 16*3^n - 48.

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