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A161938 a(n) = ((3+sqrt(2))*(2+sqrt(2))^n + (3-sqrt(2))*(2-sqrt(2))^n)/2. 2
3, 8, 26, 88, 300, 1024, 3496, 11936, 40752, 139136, 475040, 1621888, 5537472, 18906112, 64549504, 220385792, 752444160, 2569005056, 8771131904, 29946517504, 102243806208, 349082189824, 1191841146880, 4069200207872 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Second binomial transform of A162255.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

FORMULA

a(n) = 4*a(n-1) - 2*a(n-2) for n>1; a(0) = 3; a(1) = 8.

G.f.: (3-4*x)/(1-4*x+2*x^2).

From G. C. Greubel, Sep 28 2018: (start)

a(2*n) = 2^(n-1) * (Q(2*n +1) + 2*Q(2*n)), Q(m) = Pell-Lucas numbers =

A002203(m).

a(2*n+1) = 2^(n-1) * (P(2*n+2) + 2*P(2*n+1)), P(m) = Pell numbers = A000129(m). (End)

MAPLE

seq(coeff(series((3-4*x)/(1-4*x+2*x^2), x, n+1), x, n), n = 0..25); # Muniru A Asiru, Sep 28 2018

MATHEMATICA

CoefficientList[Series[(3-4*x)/(1-4*x+2*x^2), {x, 0, 50}], x] (* G. C. Greubel, Sep 28 2018 *)

PROG

(MAGMA) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((3+r)*(2+r)^n+(3-r)*(2-r)^n)/2: n in [0..23] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 01 2009

(MAGMA) I:=[3, 8]; [n le 2 select I[n] else 4*Self(n-1) - 2*Self(n-2): n in [1..30]]; // G. C. Greubel, Sep 28 2018

(PARI) x='x+O('x^50); Vec((3-4*x)/(1-4*x+2*x^2)) \\ G. C. Greubel, Sep 28 2018

(GAP) a:=[3, 8];; for n in [3..25] do a[n]:=4*a[n-1]-2*a[n-2]; od; a; # Muniru A Asiru, Sep 28 2018

CROSSREFS

Cf. A162255, A135532, A083878.

Sequence in context: A148812 A148813 A148814 * A189177 A151444 A151458

Adjacent sequences:  A161935 A161936 A161937 * A161939 A161940 A161941

KEYWORD

nonn

AUTHOR

Al Hakanson (hawkuu(AT)gmail.com), Jun 22 2009, Jun 29 2009

EXTENSIONS

Edited and extended beyond a(5) by Klaus Brockhaus, Jul 01 2009

STATUS

approved

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Last modified October 21 11:42 EDT 2019. Contains 328296 sequences. (Running on oeis4.)