A192831 Molecular topological indices of the hypercube graphs.

4, 48, 360, 2304, 13600, 76032, 407680, 2113536, 10658304, 52531200, 254003200, 1208549376, 5672083456, 26309885952, 120803328000, 549772591104, 2482528976896, 11132640165888, 49615651471360, 219902744985600, 969770180542464, 4257311052791808

Offset

1,1

Links

Andrew Howroyd, Table of n, a(n) for n = 1..200

Eric Weisstein's World of Mathematics, Hypercube Graph

Eric Weisstein's World of Mathematics, Molecular Topological Index

Index entries for linear recurrences with constant coefficients, signature (18,-132,504,-1056,1152,-512).

Formula

a(n) = 2^n*n^2*(1+2^(n-1)). - Andrew Howroyd, May 11 2017

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

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

E.g.f.: 2*x*(1 +2*x + (1 +4*x)*exp(2*x))*exp(2*x). - G. C. Greubel, Jan 04 2019

Mathematica

Table[2^n*n^2*(2^(n-1) +1), {n, 30}] (* Eric W. Weisstein, May 27 2017 *)
LinearRecurrence[{18, -132, 504, -1056, 1152, -512}, {4, 48, 360, 2304, 13600, 76032}, 30] (* Eric W. Weisstein, May 27 2017 *)

Prog

(PARI) vector(30, n, 2^n*n^2*(1+2^(n-1))) \\ G. C. Greubel, Jan 04 2019
(Magma) [2^n*n^2*(1+2^(n-1)): n in [1..30]]; // G. C. Greubel, Jan 04 2019
(Sage) [2^n*n^2*(1+2^(n-1)) for n in (1..30)] # G. C. Greubel, Jan 04 2019
(GAP) List([1..30], n -> 2^n*n^2*(1+2^(n-1))); # G. C. Greubel, Jan 04 2019

Crossrefs

Cf. A192826, A192830.

Sequence in context: A291623 A144704 A091904 * A158681 A269180 A228701

Adjacent sequences: A192828 A192829 A192830 * A192832 A192833 A192834

Keyword

nonn

Author

Eric W. Weisstein, Jul 11 2011

Extensions

a(11)-a(22) from Andrew Howroyd, May 11 2017

Status

approved