A164536 a(n) = 10*a(n-1) - 23*a(n-2) for n > 1; a(0) = 3, a(1) = 23.

3, 23, 161, 1081, 7107, 46207, 298609, 1923329, 12365283, 79416263, 509761121, 3271037161, 20985865827, 134624803567, 863573121649, 5539360734449, 35531425546563, 227908958573303, 1461866798162081, 9376761934434841

Offset

0,1

Comments

Binomial transform of A164535. Fifth binomial transform of A164654.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..151

Index entries for linear recurrences with constant coefficients, signature (10, -23).

Formula

a(n) = 10*a(n-1) - 23*a(n-2) for n > 1; a(0) = 3, a(1) = 23.

G.f.: (3-7*x)/(1-10*x+23*x^2).

a(n) = ((3+4*sqrt(2))*(5+sqrt(2))^n + (3-4*sqrt(2))*(5-sqrt(2))^n)/2.

Mathematica

LinearRecurrence[{10, -23}, {3, 23}, 30] (* or *) CoefficientList[Series[ (3-7*x)/(1-10*x+23*x^2), {x, 0, 30}], x] (* Harvey P. Dale, Dec 18 2011 *)

Prog

(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((3+4*r)*(5+r)^n+(3-4*r)*(5-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 20 2009

Crossrefs

Cf. A164535, A164654.

Sequence in context: A006184 A308677 A209011 * A037789 A037670 A037796

Adjacent sequences: A164533 A164534 A164535 * A164537 A164538 A164539

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