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%I #23 Sep 08 2022 08:45:58
%S 4,72,448,2400,13824,72128,389120,1949184,9932800,47950848,234160128,
%T 1098559488,5200642048,23876812800,110456995840,498763431936,
%U 2266990903296,10103408033792,45289255731200,199725155352576,885321097019392
%N Molecular topological indices of the folded cube graphs.
%H Andrew Howroyd, <a href="/A192826/b192826.txt">Table of n, a(n) for n = 2..200</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/FoldedCubeGraph.html">Folded Cube Graph</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MolecularTopologicalIndex.html">Molecular Topological Index</a>
%F a(n) = 2^(n-2)*n^2*(2 + 2^(n-1) - binomial(n-1,floor((n-1)/2))), for n>2. - _Andrew Howroyd_, May 11 2017
%F Conjecture: D-finite with recurrence: +(n-1)*(3171347*n-9561097)*a(n) +2*(-22257061*n^2+113080920*n-124259984)*a(n-1) +8*(25480326*n^2-186826067*n+302663821)*a(n-2) +16*(-2142117*n^2+189489004*n-548366652)*a(n-3) +64*(-46156212*n^2+185594099*n-75953597)*a(n-4) +1024*(11001336*n^2-74317052*n+114909451)*a(n-5) +1024*(-17489828*n^2+145166555*n-279390145)*a(n-6) +20480*(530179*n-1731202)*(n-6)*a(n-7)=0. - _R. J. Mathar_, Feb 21 2020
%t a[2] = 4; a[n_] := 2^(n-2)*n^2*(2 + 2^(n-1) - Binomial[n-1, Floor @ ((n-1)/2)]); Array[a, 21, 2] (* _Jean-François Alcover_, Nov 01 2017, after _Andrew Howroyd_ *)
%o (PARI) {a(n) = if(n==2, 4, 2^(n-2)*n^2*(2 +2^(n-1) -binomial(n-1, floor((n-1)/2))))}; \\ _G. C. Greubel_, Jan 03 2019
%o (Magma) [4] cat [2^(n-2)*n^2*(2 +2^(n-1) -Binomial(n-1,Floor((n-1)/2))): n in [3..30]] // _G. C. Greubel_, Jan 03 2019
%o (Sage) [4] + [2^(n-2)*n^2*(2 +2^(n-1) -binomial(n-1,floor((n-1)/2))) for n in (3..30)] # _G. C. Greubel_, Jan 03 2019
%Y Cf. A192831, A192830.
%K nonn
%O 2,1
%A _Eric W. Weisstein_, Jul 10 2011
%E a(11)-a(22) from _Andrew Howroyd_, May 11 2017
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