

A056236


(2+sqrt(2))^n + (2sqrt(2))^n.


7



2, 4, 12, 40, 136, 464, 1584, 5408, 18464, 63040, 215232, 734848, 2508928, 8566016, 29246208, 99852800, 340918784, 1163969536, 3974040576, 13568223232, 46324811776, 158162800640, 540001579008, 1843680714752, 6294719700992
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OFFSET

0,1


COMMENTS

First differences give A060995.  Jeremy Gardiner, Aug 11 2013.
Binomial transform of A002203 [Bhadouria].
The binomial transform of this sequence is 2, 6, 22, 90, 386, .. = 2*A083878(n).  R. J. Mathar, Nov 10 2013


LINKS

Table of n, a(n) for n=0..24.
P. Bhadouria, D. Jhala, B. Singh, Binomial Transforms of the kLucas Sequences and its [sic] Properties, The Journal of Mathematics and Computer Science (JMCS), Volume 8, Issue 1, Pages 8192, sequence B_2.
Index to sequences with linear recurrences with constant coefficients, signature (4,2).


FORMULA

a(n) = 4*a(n1)2*a(n2) = a(n2)a(n1)+2*A020727(n1) = 2*A006012(n) = 4*A007052(n1).
For n>2, a(n) = floor((2+sqrt(2))*a(n1)).
G.f.: 2*(12*x)/(14*x+2*x^2).
a(n)=2^(2*n)*[cos(Pi/8)^(2*n)+cos(3*Pi/8)^2*n]; also, a(n)=3*a(n1)+Sum{k=1..n2} a(k), for n>1, with a(0)=2, a(1)=4.  L. Edson Jeffery, Apr 08 2011


MATHEMATICA

LinearRecurrence[{4, 2}, {2, 4}, 30] (* Harvey P. Dale, Jan 18 2013 *)


PROG

(PARI) a(n) = 2*real((2+quadgen(8))^n);
(Sage) [lucas_number2(n, 4, 2) for n in range(37)] # Zerinvary Lajos, Jun 25 2008


CROSSREFS

Sequence in context: A126946 A113179 A214761 * A028329 A204678 A025227
Adjacent sequences: A056233 A056234 A056235 * A056237 A056238 A056239


KEYWORD

nonn,easy


AUTHOR

Henry Bottomley, Aug 11 2000


EXTENSIONS

More terms from James A. Sellers, Aug 25 2000


STATUS

approved



