A077943 Expansion of 1/(1 - 2*x + 2*x^2 - 2*x^3).

1, 2, 2, 2, 4, 8, 12, 16, 24, 40, 64, 96, 144, 224, 352, 544, 832, 1280, 1984, 3072, 4736, 7296, 11264, 17408, 26880, 41472, 64000, 98816, 152576, 235520, 363520, 561152, 866304, 1337344, 2064384, 3186688, 4919296, 7593984, 11722752, 18096128, 27934720, 43122688

Offset

0,2

Comments

a(n) gives the lower independence number of the (n+3)-halved cube graph up to at least n = 7. - Eric W. Weisstein, Dec 14 2023

Links

Table of n, a(n) for n=0..41.

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

Formula

a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3); a(0)=1, a(1)=2, a(2)=2. - Harvey P. Dale, Nov 30 2011

From R. J. Mathar, Mar 13 2021: (Start)

a(n) + a(n+1) = |A078071(n+1)|.

a(n) = (-1)^n*A077993(n). (End)

Mathematica

CoefficientList[Series[1/(1 - 2 x + 2 x^2 - 2 x^3), {x, 0, 50}], x] (* Harvey P. Dale, Nov 30 2011 *)
LinearRecurrence[{2, -2, 2}, {1, 2, 2}, 50] (* Harvey P. Dale, Nov 30 2011 *)
Table[RootSum[-2 + 2 # - 2 #^2 + #^3 &, 4 #^n - 6 #^(n + 1) + 7 #^(n + 2) &]/22, {n, 0, 20}] (* Eric W. Weisstein, Dec 14 2023 *)

Prog

(PARI) Vec(1/(1-2*x+2*x^2-2*x^3)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

Crossrefs

Cf. A078071, A077993.

Sequence in context: A306337 A326022 A346047 * A077993 A302613 A295680

Adjacent sequences: A077940 A077941 A077942 * A077944 A077945 A077946

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 17 2002

Status

approved