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A192826
Molecular topological indices of the folded cube graphs.
4
4, 72, 448, 2400, 13824, 72128, 389120, 1949184, 9932800, 47950848, 234160128, 1098559488, 5200642048, 23876812800, 110456995840, 498763431936, 2266990903296, 10103408033792, 45289255731200, 199725155352576, 885321097019392
OFFSET
2,1
LINKS
Eric Weisstein's World of Mathematics, Folded Cube Graph
Eric Weisstein's World of Mathematics, Molecular Topological Index
FORMULA
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
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
MATHEMATICA
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 *)
PROG
(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
(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
(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
CROSSREFS
Sequence in context: A095385 A375251 A071683 * A190398 A003752 A062018
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Jul 10 2011
EXTENSIONS
a(11)-a(22) from Andrew Howroyd, May 11 2017
STATUS
approved