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%I #12 Mar 02 2019 11:14:25
%S 15,56,232,1008,4432,19328,82944,349952,1454848,5978112,24352768,
%T 98594816,397479936,1597865984,6411452416,25695289344,102901940224,
%U 411899002880,1648290693120,6594803793920,26383058206720,105541162500096,422185252421632
%N The Wiener index of the graph obtained by applying Mycielski's construction to the hypercube graph Q(n) (n>=1).
%D D. B. West, Introduction to Graph Theory, 2nd ed., Prentice-Hall, NJ, 2001, p. 205.
%H R. Balakrishnan, S. F. Raj, <a href="http://dx.doi.org/10.7151/dmgt.1509">The Wiener number of powers of the Mycielskian</a>, Discussiones Math. Graph Theory, 30, 2010, 489-498 (see Theorem 2.1).
%H B. E. Sagan, Y-N. Yeh and P. Zhang, <a href="http://dx.doi.org/10.1002/(SICI)1097-461X(1996)60:5<959::AID-QUA2>3.0.CO;2-W">The Wiener Polynomial of a Graph</a>, Internat. J. of Quantum Chem., 60, 1996, 959-969.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (12,-56,128,-144,64).
%F a(n) = 6*2^(2*n) - 2^(n-2)*(4 + 12*n + n^2 + n^3).
%F G.f.: x*(15 - 124*x + 400*x^2 - 560*x^3 + 320*x^4)/((1 - 4*x)*(1 - 2*x)^4).
%e a(1)=15 because Q(1) is the 1-edge path whose Mycielskian is the cycle graph C(5) with Wiener index 5*1+5*2 = 15.
%p a := proc (n) options operator, arrow: 6*2^(2*n)-2^(n-2)*(4+12*n+n^2+n^3) end proc: seq(a(n), n = 1 .. 25);
%t LinearRecurrence[{12,-56,128,-144,64},{15,56,232,1008,4432},30] (* _Harvey P. Dale_, Mar 02 2019 *)
%K nonn,easy
%O 1,1
%A _Emeric Deutsch_, Aug 27 2013