A192826 Molecular topological indices of the folded cube graphs.

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

Andrew Howroyd, Table of n, a(n) for n = 2..200

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

Cf. A192831, A192830.

Sequence in context: A203537 A095385 A071683 * A190398 A003752 A062018

Adjacent sequences: A192823 A192824 A192825 * A192827 A192828 A192829

Keyword

nonn

Author

Eric W. Weisstein, Jul 10 2011

Extensions

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

Status

approved