A098586 a(n) = (1/2) * (5*P(n+1) + P(n) - 1), where P(k) are the Pell numbers A000129.

2, 5, 13, 32, 78, 189, 457, 1104, 2666, 6437, 15541, 37520, 90582, 218685, 527953, 1274592, 3077138, 7428869, 17934877, 43298624, 104532126, 252362877, 609257881, 1470878640, 3551015162, 8572908965, 20696833093, 49966575152, 120629983398, 291226541949

Offset

0,1

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Hermann Stamm-Wilbrandt, 4 interlaced bisections

Index entries for linear recurrences with constant coefficients, signature (3,-1,-1).

Formula

a(n) = 3*a(n-1) - a(n-2) - a(n-3) with a(0)=2, a(1)=5, a(2)=13. - Hermann Stamm-Wilbrandt, Aug 26 2014

G.f.: (2-x)/((1-x)*(1-2*x-x^2)). - Robert Israel, Aug 26 2014

a(n) = 7*a(n-2) - 7*a(n-4) + a(n-6), for n>5. - Hermann Stamm-Wilbrandt, Aug 27 2014

a(2*n-1) = A006451(2*n), for n>0. - Hermann Stamm-Wilbrandt, Aug 27 2014

a(2*n) = A124124(2*n+2). - Hermann Stamm-Wilbrandt, Aug 27 2014

a(n) = (-2+(5-3*sqrt(2))*(1-sqrt(2))^n + (1+sqrt(2))^n*(5+3*sqrt(2)))/4. - Colin Barker, Mar 16 2016

Maple

A:= LREtools[REtoproc](a(n) = 3*a(n-1) - a(n-2) - a(n-3), a(n), {a(0)=2, a(1)=5, a(2)=13}):
seq(A(n), n=0..100); # Robert Israel, Aug 26 2014

Mathematica

LinearRecurrence[{3, -1, -1}, {2, 5, 13}, 28] (* Hermann Stamm-Wilbrandt, Aug 26 2014 *)
CoefficientList[Series[(2-x)/((1-x)*(1-2*x-x^2)), {x, 0, 50}], x] (* G. C. Greubel, Feb 03 2018 *)

Prog

(PARI) Vec((2-x)/((1-x)*(1-2*x-x^2)) + O(x^50)) \\ Colin Barker, Mar 16 2016
(Magma) I:=[2, 5, 13]; [n le 3 select I[n] else 3*Self(n-1) - Self(n-2) - Self(n-3): n in [1..30]]; // G. C. Greubel, Feb 03 2018

Crossrefs

Cf. A006451, A124124.

Sequence in context: A116702 A098156 A267862 * A199812 A255170 A255630

Adjacent sequences: A098583 A098584 A098585 * A098587 A098588 A098589

Keyword

nonn,easy

Author

Creighton Dement, Oct 03 2004

Extensions

Formula supplied by Thomas Baruchel, Oct 03 2004

More terms from Emeric Deutsch, Nov 17 2004

Status

approved