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A292029
Wiener index of the n-folded cube graph.
0
1, 6, 40, 200, 1056, 4928, 23808, 107136, 494080, 2173952, 9744384, 42225664, 185679872, 795770880, 3451518976, 14668955648, 62970789888, 265876668416, 1132226150400, 4755349831680, 20120910954496, 84141991264256, 354160151101440, 1475667296256000, 6184144161734656
OFFSET
2,2
LINKS
Eric Weisstein's World of Mathematics, Folded Cube Graph
Eric Weisstein's World of Mathematics, Wiener Index
FORMULA
G.f.: (1 + 4*x - sqrt(1 - 16*x^2))/(4*(1 - 4*x)^2 (1 + 4*x)).
D-finite with recurrence: (-n+1)*a(n) + 4*(2*n-3)*a(n-1) + 64*(-2*n+5)*a(n-3) + 256*(n-3)*a(n-4) = 0. - Adapted to offset by R. J. Mathar, Feb 21 2020
a(n) = 2^(n-3)*n*(2^(n-1) - binomial(n-1, floor((n-1)/2))). - Andrew Howroyd, Sep 08 2017
MATHEMATICA
Table[2^(n - 3) n (2^(n - 1) - Binomial[n - 1, Floor[(n - 1)/2]]), {n, 2, 20}]
CoefficientList[Series[(1 + 4 x - Sqrt[1 - 16 x^2])/(4 x (1 - 4 x)^2 (1 + 4 x)), {x, 0, 20}], x]
PROG
(PARI) a(n) = 2^(n-3)*n*(2^(n-1) - binomial(n-1, floor((n-1)/2))); \\ Andrew Howroyd, Sep 08 2017
CROSSREFS
Cf. A192826.
Sequence in context: A055344 A210424 A367778 * A227124 A232568 A288637
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Sep 07 2017
STATUS
approved