|
%I #18 Sep 08 2022 08:45:58
%S 4,48,360,2304,13600,76032,407680,2113536,10658304,52531200,254003200,
%T 1208549376,5672083456,26309885952,120803328000,549772591104,
%U 2482528976896,11132640165888,49615651471360,219902744985600,969770180542464,4257311052791808
%N Molecular topological indices of the hypercube graphs.
%H Andrew Howroyd, <a href="/A192831/b192831.txt">Table of n, a(n) for n = 1..200</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HypercubeGraph.html">Hypercube Graph</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MolecularTopologicalIndex.html">Molecular Topological Index</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (18,-132,504,-1056,1152,-512).
%F a(n) = 2^n*n^2*(1+2^(n-1)). - _Andrew Howroyd_, May 11 2017
%F a(n) = 18*a(n-1) -132*a(n-2) +504*a(n-3) -1056*a(n-4) +1152*a(n-5) -512*a(n-6). - _Eric W. Weisstein_, May 27 2017
%F G.f.: 4*x*(1-6*x+6*x^2+36*x^3-80*x^4)/(1-6*x+8*x^2)^3. - _Eric W. Weisstein_, May 27 2017
%F E.g.f.: 2*x*(1 +2*x + (1 +4*x)*exp(2*x))*exp(2*x). - _G. C. Greubel_, Jan 04 2019
%t Table[2^n*n^2*(2^(n-1) +1), {n, 30}] (* _Eric W. Weisstein_, May 27 2017 *)
%t LinearRecurrence[{18,-132,504,-1056,1152,-512}, {4,48,360,2304,13600, 76032}, 30] (* _Eric W. Weisstein_, May 27 2017 *)
%o (PARI) vector(30, n, 2^n*n^2*(1+2^(n-1))) \\ _G. C. Greubel_, Jan 04 2019
%o (Magma) [2^n*n^2*(1+2^(n-1)): n in [1..30]]; // _G. C. Greubel_, Jan 04 2019
%o (Sage) [2^n*n^2*(1+2^(n-1)) for n in (1..30)] # _G. C. Greubel_, Jan 04 2019
%o (GAP) List([1..30], n -> 2^n*n^2*(1+2^(n-1))); # _G. C. Greubel_, Jan 04 2019
%Y Cf. A192826, A192830.
%K nonn
%O 1,1
%A _Eric W. Weisstein_, Jul 11 2011
%E a(11)-a(22) from _Andrew Howroyd_, May 11 2017
|
