OFFSET
1,2
COMMENTS
a(n) is the second Zagreb index of the Sierpiński [Sierpinski] sieve 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 Sieve graph S[n] is M(S[n], x, y) = 6*x^2*y^4 + (3^n - 6)*x^4*y^4.
LINKS
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 Sieve Graph
Index entries for linear recurrences with constant coefficients, signature (4,-3).
FORMULA
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
MAPLE
seq(16*3^n-48, n = 1..30);
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Nov 05 2016
STATUS
approved