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A132732 Row sums of triangle A132731. 3
1, 2, 4, 10, 24, 54, 116, 242, 496, 1006, 2028, 4074, 8168, 16358, 32740, 65506, 131040, 262110, 524252, 1048538, 2097112, 4194262, 8388564, 16777170, 33554384, 67108814, 134217676, 268435402, 536870856, 1073741766, 2147483588 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) is the number of connected induced subgraphs in the (n+1)-path complement graph. - Eric W. Weisstein, Apr 11 2018

LINKS

Table of n, a(n) for n=0..30.

Eric Weisstein's World of Mathematics, Connected Graph

Eric Weisstein's World of Mathematics, Path Complement Graph

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

Index entries for linear recurrences with constant coefficients, signature (4,-5,2).

FORMULA

Binomial transform of [1, 1, 1, 3, 1, 3, 1, 3, 1,...(3,1 repeated)].

a(n) = 2*(2^n-n) = 2*A000325(n), n>0. - R. J. Mathar, Sep 16 2017

EXAMPLE

a(3) = 10 = sum of row 3 terms of triangle A132731: (1 + 4 + 4 + 1).

a(3) = 10 = (1, 3, 3, 1) dot (1, 1, 1, 3) = (1 + 3 + 3 + 3).

MATHEMATICA

Join[{1}, Table[2 (2^n - n), {n, 20}]] (* or *)

Join[{1}, LinearRecurrence[{4, -5, 2}, {2, 4, 10}, 20]] (* or *)

CoefficientList[Series[-(1 - 2 x + x^2 + 2 x^3)/((-1 + x)^2 (-1 + 2 x)), {x, 0, 20}], x] (* Eric W. Weisstein, Apr 11 2018 *)

PROG

(PARI) a(n) = if(n==0, 1, 2*(2^n-n)); \\ Altug Alkan, Apr 12 2018

CROSSREFS

Cf. A132731.

Sequence in context: A136427 A018114 A089484 * A275447 A095214 A002525

Adjacent sequences:  A132729 A132730 A132731 * A132733 A132734 A132735

KEYWORD

nonn,easy

AUTHOR

Gary W. Adamson, Aug 26 2007

STATUS

approved

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Last modified October 19 03:34 EDT 2019. Contains 328211 sequences. (Running on oeis4.)