A164535 a(n) = 8*a(n-1) - 14*a(n-2) for n > 1; a(0) = 3, a(1) = 20.

3, 20, 118, 664, 3660, 19984, 108632, 589280, 3193392, 17297216, 93670240, 507200896, 2746223808, 14868977920, 80504690048, 435871829504, 2359908975360, 12777066189824, 69177803863552, 374543504250880

Offset

0,1

Comments

Binomial transform of A164305. Fourth binomial transform of A164654. Inverse binomial transform of A164536.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..158

Index entries for linear recurrences with constant coefficients, signature (8, -14).

Formula

a(n) = 8*a(n-1) - 14*a(n-2) for n > 1; a(0) = 3, a(1) = 20.

G.f.: (3-4*x)/(1-8*x+14*x^2).

a(n) = ((3+4*sqrt(2))*(4+sqrt(2))^n + (3-4*sqrt(2))*(4-sqrt(2))^n)/2.

Mathematica

CoefficientList[Series[(3-4x)/(1-8x+14x^2), {x, 0, 25}], x]  (* Harvey P. Dale, Feb 23 2011 *)

Prog

(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((3+4*r)*(4+r)^n+(3-4*r)*(4-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 20 2009

Crossrefs

Cf. A164305, A164654, A164536.

Sequence in context: A108911 A005096 A275796 * A001652 A128910 A037788

Adjacent sequences: A164532 A164533 A164534 * A164536 A164537 A164538

Keyword

nonn,easy

Author

Al Hakanson (hawkuu(AT)gmail.com), Aug 15 2009

Extensions

Edited and extended beyond a(5) by Klaus Brockhaus, Aug 20 2009

Status

approved