A224462 The hyper-Wiener index of Wang's helicene-based dendrimer defined pictorially as DNS_2[n] in the Shabani et al. reference.

5150, 279882, 4912058, 52877106, 437291570, 3075863058, 19424101394, 113690358162, 629297936786, 3338556446610, 17134277121938, 85638400421778, 418886606368658, 2012591878934418, 9525395433164690, 44509034884173714, 205695168792825746

Offset

1,1

References

H. Shabani, A. R. Ashrafi, I. Gutman, Geometric-arithmetic index: an algebraic approach, Studia UBB, Chemia, LV, 2010, 107-112.

Links

Table of n, a(n) for n=1..17.

Formula

a(n) = -61550 + 2^n*(30861*n^2 - 164298*n - 602830)+4^n*(59049*n^2 - 677241*n/2 + 664380).

G.f.: 2*x*(2575+91016*x+183400*x^2-872548*x^3-267848*x^4+32480*x^5) / ((1-x)*(1-2*x)^3*(1-4*x)^3).

Maple

a := proc (n) options operator, arrow: -61550+2^n*(30861*n^2-164298*n-602830)+4^n*(59049*n^2-(677241/2)*n+664380) end proc: seq(a(n), n = 1 .. 17);

Crossrefs

Cf. A224461.

Sequence in context: A251244 A188338 A213701 * A251679 A151628 A210400

Adjacent sequences: A224459 A224460 A224461 * A224463 A224464 A224465

Keyword

nonn,easy

Author

Emeric Deutsch, Jul 12 2013

Status

approved