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A277105
a(n) = (27*3^n - 63)/2.
1
9, 90, 333, 1062, 3249, 9810, 29493, 88542, 265689, 797130, 2391453, 7174422, 21523329, 64570050, 193710213, 581130702, 1743392169, 5230176570, 15690529773, 47071589382, 141214768209, 423644304690, 1270932914133, 3812798742462, 11438396227449, 34315188682410, 102945566047293, 308836698141942, 926510094425889
OFFSET
1,1
COMMENTS
a(n) is the second Zagreb index of the Hanoi graph H[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 Hanoi graph H[n] is M(H[n],x,y) = 6*x^2*y^3 + (3/2)*(3^n - 5)*x^3*y^3.
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, Hanoi Graph
FORMULA
O.g.f.: 9*x*(1 + 6*x)/((1 - x)*(1 - 3*x)).
E.g.f.: 9*(1 - exp(x))*(4 - 3*exp(x) - 3*exp(2*x))/2. - Bruno Berselli, Nov 14 2016
a(n) = 9*A116970(n+1).
MAPLE
seq((1/2)*(9*(3^(n+1)-7)), n = 1..30);
MATHEMATICA
Table[(27 3^n - 63)/2, {n, 1, 30}] (* Bruno Berselli, Nov 14 2016 *)
PROG
(Magma) [(27 3^n-63)/2: n in [1..30]]; // Bruno Berselli, Nov 14 2016
CROSSREFS
Sequence in context: A043960 A044641 A165135 * A377858 A180289 A210088
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Nov 05 2016
STATUS
approved