A221045 - OEIS

%I #9 Dec 30 2012 17:29:49

%S 10,792,22002,419568,6592794,92192136,1193312130,14623811808,

%T 172078919466,1962477443832,21832497397266,238041018275280,

%U 2552456907780666,26988260347784040,281967905150124450,2915727266397879744,29880877053048885834,303816557606831292120

%N The hyper-Wiener index of the Bethe cactus lattice graph C_n defined pictorially in the Hosoya - Balasubramanian reference.

%D K. Balasubramanian, Recent developments in tree-pruning methods and polynomials for cactus graphs and trees, J. Math. Chemistry, 4 (1990) 89-102.

%D H. Hosoya, K. Balasubramanian, Exact dimer statistics and characteristic polynomials of cacti lattices, Theor. Chim. Acta 76 (1989) 315-329.

%F a(n) = (3/2)-3^(n-1)*53+3^(2*n-2)*(64*n^2-148*n)+(97/6)*3^(2*n).

%F G.f.: 2*x*(5+241*x+495*x^2+27*x^3)/((1-x)*(1-3*x)*(1-9*x)^3). - _Bruno Berselli_, Dec 30 2012

%p a := proc (n) options operator, arrow: 3/2-53*3^(n-1)+3^(2*n-2)*(64*n^2-148*n)+(97/6)*3^(2*n) end proc: seq(a(n), n = 1 .. 18);

%Y Cf. A221044.

%K nonn,easy

%O 1,1

%A _Emeric Deutsch_, Dec 30 2012

%E Offset changed from 0 to 1 by _Bruno Berselli_, Dec 30 2012