A221003 - OEIS

%I #18 Feb 13 2024 08:15:49

%S 192133,1790789,13716357,92392837,568494213,3272754309,17914312837,

%T 94292506757,481127721093,2394073245829,11669512054917,55910670854277,

%U 264011366000773,1231270134409349,5680970473662597,25967383211403397

%N The hyper-Wiener index of the nanostar dendrimer G[n], defined pictorially in the Karbasioun-Ashrafi reference.

%H A. Karbasioun and A. R. Ashrafi, <a href="https://doi.org/10.20450/mjcce.2009.221">Wiener and detour indices of a new type of nanostar dendrimers</a>, Macedonian J. of Chemistry and Chemical Engineering 28 (2009) 49-54.

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (19,-150,636,-1560,2208,-1664,512).

%F a(n) = -6011 + 2^n*(11200*n^2 + 5920*n - 177792) + 4^n*(102400*n^2 + 51200*n + 375936).

%F G.f.: (7432704*x^6 -23912064*x^5 +31269536*x^4 -21796184*x^3 +8511316*x^2 -1859738*x +192133) / ((x-1)*(2*x-1)^3*(4*x-1)^3). [_Colin Barker_, Jan 01 2013]

%p a := proc (n) options operator, arrow: -6011+2^n*(11200*n^2+5920*n-177792)+4^n*(102400*n^2+51200*n+375936) end proc: seq(a(n), n = 0 .. 15);

%Y Cf. A221002.

%K nonn,easy

%O 0,1

%A _Emeric Deutsch_, Dec 28 2012