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A292044 Wiener index of the n-halved cube graph. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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

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

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Last modified December 1 20:10 EST 2021. Contains 349430 sequences. (Running on oeis4.)