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A290721 a(n) = 4^n - n - 1. 0
2, 13, 60, 251, 1018, 4089, 16376, 65527, 262134, 1048565, 4194292, 16777203, 67108850, 268435441, 1073741808, 4294967279, 17179869166, 68719476717, 274877906924, 1099511627755, 4398046511082, 17592186044393, 70368744177640, 281474976710631, 1125899906842598 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For n > 1, also the number of (non-null) connected induced subgraphs in the n-cocktail party graph.

LINKS

Table of n, a(n) for n=1..25.

Eric Weisstein's World of Mathematics, Cocktail Party Graph

Eric Weisstein's World of Mathematics, Connected Graph

Eric Weisstein's World of Mathematics, Vertex-Induced Subgraph

Index entries for linear recurrences with constant coefficients, signature (6, -9, 4).

FORMULA

a(n) = 4^n - n - 1.

a(n) = 6*a(n-1) - 9*a(n-2) + 4*a(n-3).

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

MATHEMATICA

Table[4^n - n - 1, {n, 20}]

LinearRecurrence[{6, -9, 4}, {2, 13, 60}, 20]

CoefficientList[Series[(-2 - x)/((-1 + x)^2 (-1 + 4 x)), {x, 0, 20}], x]

CROSSREFS

Sequence in context: A042061 A229736 A187560 * A205532 A294052 A089130

Adjacent sequences:  A290718 A290719 A290720 * A290722 A290723 A290724

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, Aug 09 2017

STATUS

approved

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Last modified October 15 07:42 EDT 2019. Contains 328026 sequences. (Running on oeis4.)