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A084157 a(n)=8a(n-1)-16a(n-2)+12a(n-4); a(0)=0, a(1)=1, a(2)=4, a(3)=22. 1
0, 1, 4, 22, 112, 556, 2704, 13000, 62080, 295312, 1401664, 6644320, 31472896, 149017792, 705395968, 3338614912, 15800258560, 74772443392, 353840161792, 1674425579008, 7923565146112, 37494981225472, 177428889407488 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Binomial transform of A084156. a(n)=(A083881(n)-A026150(n))/2.

LINKS

Table of n, a(n) for n=0..22.

Index entries for linear recurrences with constant coefficients, signature (8,-16,0,12).

FORMULA

a(n)=8a(n-1)-16a(n-2)+12a(n-4); a(0)=0, a(1)=1;

a(n)=((3+sqrt(3))^n+(3-sqrt(3))^n-(1+sqrt(3))^n-(1-sqrt(3))^n)/4;

G.f.: x(1-4x+6x^2)/((1-2x-2x^2)(1-6x+6x^2));

E.g.f. : exp(2x)sinh(x)cosh(sqrt(3)x).

MATHEMATICA

LinearRecurrence[{8, -16, 0, 12}, {0, 1, 4, 22}, 30] (* Harvey P. Dale, Feb 19 2017 *)

CROSSREFS

Cf. A084155.

Sequence in context: A244423 A144047 A077543 * A085939 A192470 A274799

Adjacent sequences:  A084154 A084155 A084156 * A084158 A084159 A084160

KEYWORD

easy,nonn

AUTHOR

Paul Barry, May 16 2003

STATUS

approved

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Last modified September 28 13:24 EDT 2020. Contains 337393 sequences. (Running on oeis4.)