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A291066 Number of edges in the n-Menger sponge graph. 2
24, 672, 14976, 311808, 6334464, 127475712, 2555805696, 51166445568, 1023731564544, 20477852516352, 409582820130816, 8191862561046528, 163838900488372224, 3276791203906977792, 65535929631255822336, 1310719437050046578688, 26214395496400372629504, 524287963971202981036032 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Also the number of maximal and maximum cliques in the n-Menger sponge graph. - Eric W. Weisstein, Dec 01 2017

LINKS

Table of n, a(n) for n=1..18.

Eric Weisstein's World of Mathematics, Edge Count

Eric Weisstein's World of Mathematics, Maximal Clique

Eric Weisstein's World of Mathematics, Maximum Clique

Eric Weisstein's World of Mathematics, Menger Sponge Graph

Index entries for linear recurrences with constant coefficients, signature (28, -160).

FORMULA

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

a(n) = 28*a(n-1) - 160*a(n-2).

G.f.: (24 x)/(1 - 28 x + 160 x^2).

MATHEMATICA

Table[2^(2 n + 1) (5^n - 2^n), {n, 20}]

LinearRecurrence[{28, -160}, {24, 672}, 20]

CoefficientList[Series[24/(1 - 28 x + 160 x^2), {x, 0, 20}], x]

CROSSREFS

Cf. A009964 (vertex count).

Sequence in context: A274957 A288816 A268473 * A160038 A322746 A184274

Adjacent sequences:  A291063 A291064 A291065 * A291067 A291068 A291069

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, Aug 17 2017

STATUS

approved

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Last modified June 1 12:52 EDT 2020. Contains 334762 sequences. (Running on oeis4.)