A292044 Wiener index of the n-halved cube graph.

0, 1, 6, 32, 160, 768, 3584, 16384, 73728, 327680, 1441792, 6291456, 27262976, 117440512, 503316480, 2147483648, 9126805504, 38654705664, 163208757248, 687194767360, 2886218022912, 12094627905536, 50577534877696, 211106232532992, 879609302220800, 3659174697238528

Offset

1,3

Comments

a(n) is the sum of the first 2^(n-1) entries of A116640. - Joe Slater, Apr 11 2018

Links

Table of n, a(n) for n=1..26.

Eric Weisstein's World of Mathematics, Halved Cube Graph.

Eric Weisstein's World of Mathematics, Wiener Index.

Index entries for linear recurrences with constant coefficients, signature (8,-16).

Formula

a(n) = 2^(2*n-5)*n for n > 1.

a(n) = 8*a(n-1) - 16*a(n-2) for n > 3.

G.f.: ((1 - 2 x) x^2)/(1 - 4 x)^2.

a(n) = 4*a(n-1) + 2^(2*n-5) for n > 2. - Joe Slater, Apr 11 2018

From Amiram Eldar, Apr 16 2022: (Start)

Sum_{n>=2} 1/a(n) = 32*log(4/3) - 8.

Sum_{n>=2} (-1)^n/a(n) = 8 - 32*log(5/4). (End)

From Stefano Spezia, Aug 04 2022: (Start)

E.g.f.: (exp(4*x) - 1)*x/8.

a(n) = (-1)^n*det(M(n-1))/2 for n > 1, where M(n) is the n X n symmetric Toeplitz matrix whose first row consists of 2, 4, ..., 2*n. (End)

Mathematica

Table[If[n == 1, 0, 2^(2 n - 5) n], {n, 40}]
Join[{0}, LinearRecurrence[{8, -16}, {1, 6}, 20]]
CoefficientList[Series[((1 - 2 x) x)/(1 - 4 x)^2, {x, 0, 20}], x]

Prog

(PARI) a(n) = if(n<2, n-1, 2^(2*n-5)*n); \\ Altug Alkan, Apr 12 2018

Crossrefs

Cf. A116640.

Sequence in context: A046725 A232331 A231992 * A006668 A232494 A037530

Adjacent sequences: A292041 A292042 A292043 * A292045 A292046 A292047

Keyword

nonn,easy

Author

Eric W. Weisstein, Sep 08 2017

Status

approved