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A192831
Molecular topological indices of the hypercube graphs.
3
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
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
Sequence in context: A291623 A144704 A091904 * A158681 A269180 A228701
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Jul 11 2011
EXTENSIONS
a(11)-a(22) from Andrew Howroyd, May 11 2017
STATUS
approved