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A277106
a(n) = 8*3^n - 12.
1
12, 60, 204, 636, 1932, 5820, 17484, 52476, 157452, 472380, 1417164, 4251516, 12754572, 38263740, 114791244, 344373756, 1033121292, 3099363900, 9298091724, 27894275196, 83682825612, 251048476860, 753145430604, 2259436291836, 6778308875532
OFFSET
1,1
COMMENTS
a(n) is the first Zagreb index of the Sierpiński [Sierpinski] Sieve graph S[n].
The first Zagreb index of a simple connected graph is the sum of the squared degrees of its vertices. Alternately, it is the sum of the degree sums d(i)+d(j) over all edges ij of the graph.
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.
I. Gutman and K. C. Das, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem. 50, 2004, 83-92.
Eric Weisstein's World of Mathematics, Sierpiński Sieve Graph
FORMULA
G.f.: 12*x*(1 + x)/((1 - x)*(1 - 3*x)).
a(n) = 4*a(n-1) - 3*a(n-2).
a(n)=12*A048473(n-1). - R. J. Mathar, Apr 07 2022
MAPLE
seq(8*3^n-12, n = 1..30);
MATHEMATICA
Array[8*3^# - 12 &, 25] (* Robert G. Wilson v, Nov 05 2016 *)
LinearRecurrence[{4, -3}, {12, 60}, 40] (* Harvey P. Dale, Oct 25 2020 *)
CROSSREFS
Cf. A277107.
Sequence in context: A061624 A213818 A004302 * A000554 A012289 A012583
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Nov 05 2016
STATUS
approved